Question

Does there exist a sum formula of a geometric infinite series?

Answer 1

the ratio,r should satisfy the following condition for that
| r| < 1

Answer 2

Okay, it does.

Answer 3

For example,\[\rm \large{1} + {1 \over 3}+ {1 \over 9} +{ 1 \over 27}\cdots \]

Answer 4

formulla is
a/(1-r)

where a and r have their usual meanings..

Answer 5

U mean sum formula?

Answer 6

yes.

Answer 7

\[\large \rm {1 - r^n \over 1 - r}\]So, how to derive that ^^ formula from this one?

Answer 8

I mean, how to derive\[\large\rm {a\over 1 - r}\]from the usual formula given above?

Answer 9

since |r| < 1
and n tends to infinity,,

hope you can verify

r^n --> 0

Answer 10

Yes... a limit... yes.

Answer 11

and that gives us our simplified form/ans..

Answer 12

Oh! That was very easy. lol

Answer 13

Oops, yes.

Answer 14

Gotcha