Find all values of x for which the series converges, and find the sum of the series for those values of x

Question

anonymous · Answer

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anonymous · Answer

need some help with answering the second part :/

hartnn · Answer

wouldn't you consider it a geometric series with some common ratio ??
try to find the common ratio 'r'
then the sum formula is simple,
$\large S_\infty = \dfrac{a}{1-r}$

anonymous · Answer

@hartnn i attempted to figure out the formula for this series and i came up with ...

anonymous · Answer

(-1)^k x^(13n+1)

anonymous · Answer

not sure if that is correct ?

hartnn · Answer

try this.,...
r= -x^14/x = - x^13

S = x/(1- (-x^13)) = x/ (1+x^13)

anonymous · Answer

let me try that! however, now i understand what they were doing in the book examples! i was stumped