Question

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

Answer 1

need some help with answering the second part :/

Answer 2

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,
\(\large S_\infty = \dfrac{a}{1-r}\)

Answer 3

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

Answer 4

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

Answer 5

not sure if that is correct ?

Answer 6

try this.,...
r= -x^14/x = - x^13

S = x/(1- (-x^13)) = x/ (1+x^13)

Answer 7

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