Infinite summation

Calculus Level 1

$1+\frac { 1 }{ 4 } +\frac { 1 }{ 16 } +\frac { 1 }{ 64 } + \cdots$

Evaluate the geometric series above.

2

\frac{3}{4}

\frac{3}{2}

\frac{4}{3}

\frac{1}{2}

2 solutions

Sumukh Bansal
Nov 8, 2017

$\large \displaystyle \sum_{n=0}^{\infty}\frac{1}{4^n}=\frac{a}{1-r}=\frac{1}{1-\frac{1}{4}}=\color{#20A900}\boxed{\frac{4}{3}}$

Good solution...

Md Mehedi Hasan - 3 years, 7 months ago

Could you tell me if this problem and its answer is correct Thanks for any help.,

Sumukh Bansal - 3 years, 7 months ago

Md Mehedi Hasan
Nov 2, 2017

$S_{\infty}=\frac{a}{1-r}=\frac{1}{1-\frac{1}{4}}=\frac{1}{\frac{4-1}{4}}=\boxed{\frac{4}{3}}$