10. 1²+2²+...+ n² = n(n+1)(2n + 1) 6 integer n ≥ 1. s 12 for every
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
#10 please, please explain in best detail please
![of the
ht-hand
true.
rue
1
³(k)
thesis.]
We
1)
a
1)
a, br
was to
Enduc-
t is
e its
nemati-
1 or
induction.
10. 1²+2²+...+ n² =
for every
integer n ≥ 1.
3
11. 1³+2³+ + n³ =
, for every integer
n≥ 1.
PATCH KONG
1
1
n
1 1
+
12.
+...+
for every
n+1'
1.2 2.3
n(n+1)
norw
integer n ≥ 1.
ss
n-1
13. i(i+1)=
n(n-1)(n+1)
3
, for every integer es
i=1
1209
moizoq this
n≥ 2.
QE
n+1
14. i. 2¹ = n.2"+2+2, for every integer n ≥ 0.
i=1
n
H 15. Σi(i!) = (n + 1)! - 1, for every integer n ≥ 1.
i=1
1
n+1
16. | 1
1
(¹-2)(¹-3) -·-·(¹-2) -
2n
-, for every
n
T-
integer n ≥ 2.
ES
instrated i ovog s sh
1 1
n
00
1
17. II
2i+1 2+2
i=0
n≥ 0.
(2n+2)!'
boig sdi to toulav
for every integer
100 SE
n
Dede
1
İ(₁-
-
for every integer n ≥ 2.
i=2
n
section.
Hint: See the discussion at the beginning of this
16m
19. (For students who have studied calculus) Use
mathematical induction, the product rule from
= 1 and that
d(x)
calculus, and the facts that
k+1
k
dx
X
d(x") n-]
= x.x to prove that for every integer n ≥ 1,
dx
= nx
18.
n(n + 1)(2n + 1)
6
n(n+1)
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7daa69d8-205a-4b72-abf5-96966d755823%2F1f455424-e7bd-4cba-b611-751f62d12c48%2Fl5x7v1l.jpeg&w=3840&q=75)
Transcribed Image Text:of the
ht-hand
true.
rue
1
³(k)
thesis.]
We
1)
a
1)
a, br
was to
Enduc-
t is
e its
nemati-
1 or
induction.
10. 1²+2²+...+ n² =
for every
integer n ≥ 1.
3
11. 1³+2³+ + n³ =
, for every integer
n≥ 1.
PATCH KONG
1
1
n
1 1
+
12.
+...+
for every
n+1'
1.2 2.3
n(n+1)
norw
integer n ≥ 1.
ss
n-1
13. i(i+1)=
n(n-1)(n+1)
3
, for every integer es
i=1
1209
moizoq this
n≥ 2.
QE
n+1
14. i. 2¹ = n.2"+2+2, for every integer n ≥ 0.
i=1
n
H 15. Σi(i!) = (n + 1)! - 1, for every integer n ≥ 1.
i=1
1
n+1
16. | 1
1
(¹-2)(¹-3) -·-·(¹-2) -
2n
-, for every
n
T-
integer n ≥ 2.
ES
instrated i ovog s sh
1 1
n
00
1
17. II
2i+1 2+2
i=0
n≥ 0.
(2n+2)!'
boig sdi to toulav
for every integer
100 SE
n
Dede
1
İ(₁-
-
for every integer n ≥ 2.
i=2
n
section.
Hint: See the discussion at the beginning of this
16m
19. (For students who have studied calculus) Use
mathematical induction, the product rule from
= 1 and that
d(x)
calculus, and the facts that
k+1
k
dx
X
d(x") n-]
= x.x to prove that for every integer n ≥ 1,
dx
= nx
18.
n(n + 1)(2n + 1)
6
n(n+1)
2
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