n-2 2р + h П fei+sP+ föi+7h` föi+7P + f6i+6h, föi+49 + f6i+3k \ f6i+39 + f6i+2k / X6n-2 p+h i=0 n-2 2p+h P+h П f6i+sp+ f6i+7h f6i+7p+ f6i+6h föi+49+f6i+3k f6i+39+f6i+2k h r i=0 h + fonq+fên-1k h fön+19+f6nk п-2 2р + h П fei+8P + f6i+7h fei+49 + f6i+3k foi+39 + föi+2k, X6n-2 p+h föi+7P + f6i+6h) i=0 п-2 2p+h p+h IT ( foi+sp+fei+7h f6i+7p+f6i+6h i=0 h r f6i+49+f6i+3k f6i+39+f6i+2k fönq+fén-1k fên+19+f6nk h1+ n-2 (foi+8P+ f6i+7h` foi+7P + f6i+6h, 2р + h П föi+49 + f6i+3k` föi+39 + fei+2k , p+h i=0 n-2 2p+h P+h П f6i+8p+f6i+7h fei+7p+f6i+6h f6i+49+ f6i+3k f6i+39+f6i+2k i=0 fön+19+f6nk+f6nq+f6n-1k fén+19+f6nk
n-2 2р + h П fei+sP+ föi+7h` föi+7P + f6i+6h, föi+49 + f6i+3k \ f6i+39 + f6i+2k / X6n-2 p+h i=0 n-2 2p+h P+h П f6i+sp+ f6i+7h f6i+7p+ f6i+6h föi+49+f6i+3k f6i+39+f6i+2k h r i=0 h + fonq+fên-1k h fön+19+f6nk п-2 2р + h П fei+8P + f6i+7h fei+49 + f6i+3k foi+39 + föi+2k, X6n-2 p+h föi+7P + f6i+6h) i=0 п-2 2p+h p+h IT ( foi+sp+fei+7h f6i+7p+f6i+6h i=0 h r f6i+49+f6i+3k f6i+39+f6i+2k fönq+fén-1k fên+19+f6nk h1+ n-2 (foi+8P+ f6i+7h` foi+7P + f6i+6h, 2р + h П föi+49 + f6i+3k` föi+39 + fei+2k , p+h i=0 n-2 2p+h P+h П f6i+8p+f6i+7h fei+7p+f6i+6h f6i+49+ f6i+3k f6i+39+f6i+2k i=0 fön+19+f6nk+f6nq+f6n-1k fén+19+f6nk
Related questions
Question
Show me the steps of determine blue and information is here step by step
![п-2
2р + h
П
föi+49 + f6i+3k`
fsi+39 + föi+2k ,
foi+8P + fei+7h`
)
X6n-2
p+h
fei+7P
+ fei+6h,
i=0
п-2
-() II
2p+h
f6i+8p+f6i+7h
fei+7p+f6i+6h
i=0
föi+49+f6i+3k
f6i+39+f6i+2k
h r
p+h
+
fönq+ fên-1k
h
fon+19+fönk
h+ P
п-2
foi+8P + fói+7h
П
fei+7P + fei+6h,
( föi+49 + f6i+3k
foi+39 + fei+2k,
2р + h
X6n-2
p+h
i=0
п-2
2p+h
p+h
П
f6i+8p+f6i+7h
fei+7p+f6i+6h
f6i+49+ƒ6i+3k
fei+39+f6i+2k
h r
i=0
fönq+ fén-1k
fön+19+fénk
h|1+
п-2
foi+8P + foi+7h`
П
foi+7P + fói+6h ,
föi+49 + f6i+3k`
föi+39 + f6i+2k ,
2р + h
X6n-2
p+h
i=0
п-2
2p+h
p+h
П
f6i+8p+f6i+7h
f6i+7p+ f6i+6h
foi+49+f6i+3k
fei+39+f6i+2k
i=0
+
fon+19+f6nk+fënq+fên–1k
fon+19+ fönk
п-2
foitsP + fói+7h
foi+7P + f6i+6h
foi+49 + f6i+3k
fei+39 + fei+2k,
2р + h
p+h
i=0
n-2
2p+h
p+h
П
f6i+8p+f6i+7h
f6i+7p+f6i+6h
fei+49+f6i+3k
foi+39+f6i+2k /
i=0
fön+29+fön+1k
fön+19+f6nk
п-2
2р + h
П
foi+sP + föi+7h
foi+rP + fei+sh ) Foi+39 + foi+2k ,
(foi+49 + fói+3k
fön+19 + fönk
1+
p+h
fon+29 + fön+1k ]
i=0
п-2
2р + h
П
foi+8P + f6i+7h`
foi+7P+ foi+ch ) \ foi+39 + föi+2k /
(foi+49 + fói+3k \ [ fön+29 + fön+1k + fon+19 + fönk
=
r
p+h
fön+29 + fön+1k
i=0
п-2
föi+8P + f6i+7h`
П
Jöi+7P + fei+6h ) Cein2g i fn) Tôn+39 + fön+2k]
(2р + h
foi+49 + föi+3k`
p+h
[ fön+29 + fön+1k ]
i=0
16](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F158aed3a-44ed-4147-bb6c-9729d6a7101b%2F516624c7-2fc9-484a-8d7e-af780273a6f6%2Fy5e12tm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:п-2
2р + h
П
föi+49 + f6i+3k`
fsi+39 + föi+2k ,
foi+8P + fei+7h`
)
X6n-2
p+h
fei+7P
+ fei+6h,
i=0
п-2
-() II
2p+h
f6i+8p+f6i+7h
fei+7p+f6i+6h
i=0
föi+49+f6i+3k
f6i+39+f6i+2k
h r
p+h
+
fönq+ fên-1k
h
fon+19+fönk
h+ P
п-2
foi+8P + fói+7h
П
fei+7P + fei+6h,
( föi+49 + f6i+3k
foi+39 + fei+2k,
2р + h
X6n-2
p+h
i=0
п-2
2p+h
p+h
П
f6i+8p+f6i+7h
fei+7p+f6i+6h
f6i+49+ƒ6i+3k
fei+39+f6i+2k
h r
i=0
fönq+ fén-1k
fön+19+fénk
h|1+
п-2
foi+8P + foi+7h`
П
foi+7P + fói+6h ,
föi+49 + f6i+3k`
föi+39 + f6i+2k ,
2р + h
X6n-2
p+h
i=0
п-2
2p+h
p+h
П
f6i+8p+f6i+7h
f6i+7p+ f6i+6h
foi+49+f6i+3k
fei+39+f6i+2k
i=0
+
fon+19+f6nk+fënq+fên–1k
fon+19+ fönk
п-2
foitsP + fói+7h
foi+7P + f6i+6h
foi+49 + f6i+3k
fei+39 + fei+2k,
2р + h
p+h
i=0
n-2
2p+h
p+h
П
f6i+8p+f6i+7h
f6i+7p+f6i+6h
fei+49+f6i+3k
foi+39+f6i+2k /
i=0
fön+29+fön+1k
fön+19+f6nk
п-2
2р + h
П
foi+sP + föi+7h
foi+rP + fei+sh ) Foi+39 + foi+2k ,
(foi+49 + fói+3k
fön+19 + fönk
1+
p+h
fon+29 + fön+1k ]
i=0
п-2
2р + h
П
foi+8P + f6i+7h`
foi+7P+ foi+ch ) \ foi+39 + föi+2k /
(foi+49 + fói+3k \ [ fön+29 + fön+1k + fon+19 + fönk
=
r
p+h
fön+29 + fön+1k
i=0
п-2
föi+8P + f6i+7h`
П
Jöi+7P + fei+6h ) Cein2g i fn) Tôn+39 + fön+2k]
(2р + h
foi+49 + föi+3k`
p+h
[ fön+29 + fön+1k ]
i=0
16
![Brn-1In-2
YIn-1 + &xn-4
In+1 = a1n-2 +
n = 0, 1,...,
(1)
1
The following special case of Eq.(1) has been studied
In-1In-2
Int1 = In-2+
(8)
Tn-1 + In-4
where the initial conditions r-4, I-3, T-2, T-1,and xo are arbitrary non zero real
numbers.
Theorem 4. Let {zn}-4 be a solution of Eq.-(8). Then for n = 0, 1,2, ...
fep + fes-ih ( foi+29 + foiik
Jei-1p+ fei-zh)
fo419 + Sauk)
farq + Sai-1k
feirap + forah ) To-19 + foi-ak ,
(Sei+aP + fot+3h)
fei-2P + fei+1h (foi+19 + Sei+ak
= rT
fei+1P+ fesh ) Joi+39 + fei+2k )
(fei+ep + fes+sh\ (foi+29 + fei+ik
Soi-sp + feisah)
fei+ap + fei+ah\ ( feiseq + fei-sk
Sai+ap + fei+2h ) Jai459 + Seisak )
fei+19 + fask
2p +h
II ap+ fesch) (Tars9 + Suvzk,
foi+sP + fouth ( Seisa9 + Soirak
In+1 =
p+h
where r-4 = h, r-3 = k, z-2 = r, r-1 = P, 2o = q, {fm}-1 = {1,0,1,1,2, 3, 5, 8, .}.
Proof: For n -0 the result holds. Now suppose that n>0 and that our assumption
holds for n - 2. That is;
feirap + foi+ah
Jei+ap + fei42h) J6i-19 + fei-2k
fauq + foi-1 k
i-0
fai+1p + fesh ) fet439 + feirak)
Joi+ep + fei+sh (fei+29 + foi+zk
foi+sp + fes+ah)
Iom-6 = 9TT(fei-4p + foi+3h (fei+09 + fei-sk
+ fei+zh) \Torr39 + fei+ak ) *
(2p + h ( foi-sp+ fesuzh (foir49 + foi+ak
Ji+7p + Soisgh) Tausg + Soi+zk
p+h
Now, it follows from Eq.(8) that
IGn-4 = Iộn-7 +
11
feisep + fo+sh ( foi+29 + fe+ik
Sunsp + Seissh ) (Tus1g+ fesk)
= p||
•II )( )II( ) )
(foi+op + fou-sh ( fei-29 + fei+ikY
1foi+sp + foi+sh)
foi+19 + fosk
+ A
PIT fasop + foish) ( for-29 + Sousik
Joi4sp+fostah)
n-2
= p
Fei+sp + feirah)
feir19 + faik
pg
( foi+6P + fei+sh) ( fei+29 + fei-ik
=PlI(asp+ fash)( Far1q + Sak )
12
PII
´ fouvap + faunh\ ( fa-29 + feieik)
Sos+19 + Souk
PIIusp + Jourah)
1+ (
PII( ) )
-PT (furep + fouosh (fau29 + fuosk
Sei-sp + foi-gh )
fois19 + fuk)
n-2
PII( (unt
Jeusp + Sanah)
Sesig+ fauk
(An
( fesep + fursh ( fev29 + Jairak1+a+ fon-ek
- PII
Sen-o9 + fon-zk]
n-2
Sen-s9 + Son -ak-"
Sei+ep + Sei+sh) ( Su-29 + Sai+ik [ Sen-sq + Sen-sk
= PII(sp+ fursh)Tuer9+ feck ) [Ton-39 + Sen-sk]
Therefore
R-1
Also, from Eq.(8), we see that
Tusap + Seurzli ) ( Jonnog + Senek )
( )--II( )( )
13](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F158aed3a-44ed-4147-bb6c-9729d6a7101b%2F516624c7-2fc9-484a-8d7e-af780273a6f6%2Fikmnef_processed.png&w=3840&q=75)
Transcribed Image Text:Brn-1In-2
YIn-1 + &xn-4
In+1 = a1n-2 +
n = 0, 1,...,
(1)
1
The following special case of Eq.(1) has been studied
In-1In-2
Int1 = In-2+
(8)
Tn-1 + In-4
where the initial conditions r-4, I-3, T-2, T-1,and xo are arbitrary non zero real
numbers.
Theorem 4. Let {zn}-4 be a solution of Eq.-(8). Then for n = 0, 1,2, ...
fep + fes-ih ( foi+29 + foiik
Jei-1p+ fei-zh)
fo419 + Sauk)
farq + Sai-1k
feirap + forah ) To-19 + foi-ak ,
(Sei+aP + fot+3h)
fei-2P + fei+1h (foi+19 + Sei+ak
= rT
fei+1P+ fesh ) Joi+39 + fei+2k )
(fei+ep + fes+sh\ (foi+29 + fei+ik
Soi-sp + feisah)
fei+ap + fei+ah\ ( feiseq + fei-sk
Sai+ap + fei+2h ) Jai459 + Seisak )
fei+19 + fask
2p +h
II ap+ fesch) (Tars9 + Suvzk,
foi+sP + fouth ( Seisa9 + Soirak
In+1 =
p+h
where r-4 = h, r-3 = k, z-2 = r, r-1 = P, 2o = q, {fm}-1 = {1,0,1,1,2, 3, 5, 8, .}.
Proof: For n -0 the result holds. Now suppose that n>0 and that our assumption
holds for n - 2. That is;
feirap + foi+ah
Jei+ap + fei42h) J6i-19 + fei-2k
fauq + foi-1 k
i-0
fai+1p + fesh ) fet439 + feirak)
Joi+ep + fei+sh (fei+29 + foi+zk
foi+sp + fes+ah)
Iom-6 = 9TT(fei-4p + foi+3h (fei+09 + fei-sk
+ fei+zh) \Torr39 + fei+ak ) *
(2p + h ( foi-sp+ fesuzh (foir49 + foi+ak
Ji+7p + Soisgh) Tausg + Soi+zk
p+h
Now, it follows from Eq.(8) that
IGn-4 = Iộn-7 +
11
feisep + fo+sh ( foi+29 + fe+ik
Sunsp + Seissh ) (Tus1g+ fesk)
= p||
•II )( )II( ) )
(foi+op + fou-sh ( fei-29 + fei+ikY
1foi+sp + foi+sh)
foi+19 + fosk
+ A
PIT fasop + foish) ( for-29 + Sousik
Joi4sp+fostah)
n-2
= p
Fei+sp + feirah)
feir19 + faik
pg
( foi+6P + fei+sh) ( fei+29 + fei-ik
=PlI(asp+ fash)( Far1q + Sak )
12
PII
´ fouvap + faunh\ ( fa-29 + feieik)
Sos+19 + Souk
PIIusp + Jourah)
1+ (
PII( ) )
-PT (furep + fouosh (fau29 + fuosk
Sei-sp + foi-gh )
fois19 + fuk)
n-2
PII( (unt
Jeusp + Sanah)
Sesig+ fauk
(An
( fesep + fursh ( fev29 + Jairak1+a+ fon-ek
- PII
Sen-o9 + fon-zk]
n-2
Sen-s9 + Son -ak-"
Sei+ep + Sei+sh) ( Su-29 + Sai+ik [ Sen-sq + Sen-sk
= PII(sp+ fursh)Tuer9+ feck ) [Ton-39 + Sen-sk]
Therefore
R-1
Also, from Eq.(8), we see that
Tusap + Seurzli ) ( Jonnog + Senek )
( )--II( )( )
13
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
