Question

Find the sum of the infinite series 1/3+4/9+16/27+64/81+... if it exists

Answer 1

well it would appear that the common ratio is

\[r = \frac{4}{3}\]

since r > 1 then the series will diverge...

Answer 2

what do u mean if it exists?

Answer 3

well if the series has a value of r such that

-1 < r < 1

then the series converges and you can find an infinite sum

Answer 4

first find q.
\[q=\frac{ 4 }{ 9 }\div \frac{ 1 }{ 3 }=\frac{ 4 }{ 3 }\]
when q>1 we use this formula
\[s _{n}=\frac{ q^n-1}{ q-1 }\]
but we don't have n so we can't find the sum.

Answer 5

This is an infinite series. n -> infinity.

Answer 6

Since this is a divergent series there is no sum.

Answer 7

thank you

Answer 8

glad to help