In: Advanced Math
1. a.) Find the values of x for which the series converges. Express your answer in interval notation. n = 1 ∞ ∑(−3)n?n
b.) Find the sum of the series (valid over the values of x found in part a).
1.
(a). Given series
.
If
be the radius of convegence of the above series then ,
Now at
the series is
which is an divergent series .
At the
series is
which is an divergent series .
Hence the interval of convergence of the given series is
.
Answer :
.
(b). Sum of the series ,
, which is an geometric series with common ratio -3x .
, as
.
Hence the required sumof the series is
.
Answer :
.
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.
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If you have doubt or need more clarification at any step please comment .