Question

please help me


how is this series converging ??
https://www.dropbox.com/s/ewm8pl948hljtoi/Screenshot%202016-04-02%2016.26.57.png?dl=0

Answer 1

@Kainui

Answer 2

Might be good if you explain why you think it's not converging.

Answer 3

first off \(5^3\)is just a number right it is \(125\)

Answer 4

write as a fraction, you will see it

Answer 5

I can show you how to evaluate it too, although there are probably other ways of figuring it out. The main trick to evaluating it is this:

\[(1-x)^{-1} = \sum_{k=0}^\infty x^k\]\[\frac{d}{dx} (1-x)^{-1} = \sum_{k=0}^\infty kx^{k-1}\]

Answer 6

this is a geometric series with ratio = 5^3 * 1/6 ........ right ????

@Kainui

Answer 7

The ratio is \[\frac{a_{k+1}}{a_k}\]

Answer 8

why not 5^3 * 1/6

Answer 9

I thought if we keep multiplying 5^3 ( the first term) with the same thing above we get the series

Answer 10

hence it being geometric

Answer 11

has a common ration