Tutorial 2
Math 262
Problem 1
Determine whether the following infinite series converge or diverge. If it converges, find the sum.
a)
∑
("#)
!"#
%
#!$%
&
'()
b)
∑
)
'
#
")
&
'(%
Problem 2
Determine whether the following infinite series converge or diverge.
a)
∑
*+,(')
'
#
-)
&
'()
e)
∑
)
'
sin %
)
'
#
&
&
'()
b)
∑
('!)
#
(%')!
&
'()
f)
∑
%2
%
!
− 1&
&
'()
c)
∑
%
/'")
0'-)
&
!
#
&
'()
g)
∑
%1 +
)
'
&
'
&
'()
d)
∑
√'-2
'
#
"3'-%
&
'()
h)
∑
)
45(' 45('))
&
'(%
Problem 3
Consider the infinite series
∑
)
'(45('))
#
&
'(%
.
a) Prove the series converges using the Integral Test.
b) Approximate the sum within an error of 0.8.
