Given the function is defined by, f(n)=1+0.6^{2}+0.6^{3}+0.6^{4}+0.6^{5}+...+0.6^{n-1}+0.6^{n }How can I define it in a more definite way and shorter? Help please!

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- Apr 26th 2013, 05:30 AMyugimutoshungProblem on function definition
Given the function is defined by, f(n)=1+0.6

^{2}+0.6^{3}+0.6^{4}+0.6^{5}+...+0.6^{n-1}+0.6^{n }How can I define it in a more definite way and shorter? Help please! - Apr 26th 2013, 05:36 AMPlatoRe: Problem on function definition
- Apr 26th 2013, 05:37 AMProve ItRe: Problem on function definition
You could write it as $\displaystyle \displaystyle \begin{align*} f(n) = \sum_{k = 0}^{n} \left( \frac{3}{5} \right) ^k - \frac{3}{5} \end{align*}$, and this sum is a finite geometric series, and so its sum can be found using the finite geometric series formula.

- Apr 26th 2013, 05:39 AMyugimutoshungRe: Problem on function definition
OMG thank you so much! I tried numerical method but failed for hours

- Apr 26th 2013, 05:47 AMyugimutoshungRe: Problem on function definition
what about f(n) = 1 + 2(0.6)^1 + 2(0.6)^2 + (0.6)^3 + ... + 2(0.6)^n ?

- Apr 26th 2013, 06:02 AMProve ItRe: Problem on function definition
- Apr 26th 2013, 06:04 AMyugimutoshungRe: Problem on function definition
I forgot the formula... So how can I do it?

- Apr 26th 2013, 10:28 AMemakarovRe: Problem on function definition