Some sequences are defined by a recursion formula —that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if { a n } is defined by a 1 = 1 a n d a n = 2 a n − 1 + 1 f o r n ≥ 2 then a 2 = 2 a 1 + 1 = 2 ⋅ 1 + 1 = 3 a 3 = 2 a 2 + 1 = 2 ⋅ 3 + 1 = 7 a 4 = 2 a 3 + 1 = 2 ⋅ 7 + 1 = 15 and so on. In Problems 63–66, write the first five terms of each sequence. 63. a 1 = 3 and a n = 2 a n – 1 – 2 for n ≥ 2
Some sequences are defined by a recursion formula —that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if { a n } is defined by a 1 = 1 a n d a n = 2 a n − 1 + 1 f o r n ≥ 2 then a 2 = 2 a 1 + 1 = 2 ⋅ 1 + 1 = 3 a 3 = 2 a 2 + 1 = 2 ⋅ 3 + 1 = 7 a 4 = 2 a 3 + 1 = 2 ⋅ 7 + 1 = 15 and so on. In Problems 63–66, write the first five terms of each sequence. 63. a 1 = 3 and a n = 2 a n – 1 – 2 for n ≥ 2
Solution Summary: The author explains that the first five terms of the sequence a_n are 2, 4, 6, 10 and 18. Since the value of n starts from 2, compute the term for
Some sequences are defined by arecursion formula—that is, a formula that defines each term of the sequence in terms of one or more of the preceding terms. For example, if {an} is defined by
a
1
=
1
a
n
d
a
n
=
2
a
n
−
1
+
1
f
o
r
n
≥
2
then
a
2
=
2
a
1
+
1
=
2
⋅
1
+
1
=
3
a
3
=
2
a
2
+
1
=
2
⋅
3
+
1
=
7
a
4
=
2
a
3
+
1
=
2
⋅
7
+
1
=
15
and so on. In Problems 63–66, write the first five terms of each sequence.
3) Let G be the group generated by elements a and b satisfying the relations a² = 63,
66 = 1, and a ¹ba = b¹. Which of the following is equivalent to the element
z = a a-2ba3b3?
A) b-2a-1
B) ab²
C) ab
D) ba
E) b²a
1) Find all complex solutions to cos(z)
=
3) Compute
where C is the circle |z― i|
=
-
1
2
2+1
Po z z
-
2)2
dz
traversed counterclockwise.
Solution: TYPE YOUR SOLUTION HERE! INCLUDE A SKETCH OF THE COM-
PLEX PLANE AND THE CURVE C. ALSO, MARK ALL SINGULARITIES OF THE
INTEGRAND!
Chapter B.1 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
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