Question

(over:∞)Σ(under:n=1) (1/3)^n
What makes this into (1/2)<∞ ? I dont get the connection.... Can anyone explain?

Answer 1

is it
\[\sum_{\infty}^{n=1} (\frac{ 1 }{ 3 })^{n}\] ...????

Answer 2

other way around n=1 is under, but the rest, yes.

Answer 3

Found it! :D

\[\sum_{n=1}^{\infty} (\frac{ 1 }{ 3 })^{n} equals \sum_{n=0}^{\infty} (\frac{ 1 }{ 3 })*(\frac{ 1 }{ 3 })^{n} \]
And that equals \[\frac{ \frac{ 1 }{ 3 } }{ 1-\frac{ 1 }{ 3 } } equals \frac{ 1 }{ 2 }\]