aysenurgökhan 21:48 24 Mar 2013 #1 
mathematics21 22:20 24 Mar 2013 #2 8)
i)
ii)
i)
ii)
mathematics21 22:28 24 Mar 2013 #3 9)
i) The series
converges when |4x|<1. That is, if -1/4 < x < 1/4 the given geometric series converges. To find the sum of the series, we shift the index:
The other two can be done in the same way.
i) The series
∞
∑
n=1
4nxn=
∞
∑
n=1
(4x)n
converges when |4x|<1. That is, if -1/4 < x < 1/4 the given geometric series converges. To find the sum of the series, we shift the index:
∞
∑
n=1
(4x)n=
∞
∑
n=0
(4x)n+1=(4x)
∞
∑
n=0
(4x)n=
4x
1-4x
The other two can be done in the same way.