MHB Calculate the sum for the infinite geometric series

[karush]

Calculate the sum for the infinite geometric series
$4+2+1+\frac{1}{2}+...$

all I know is the ratio is $\frac{1}{2}$

$\displaystyle\sum_{n}^{\infty}a{r}^{n}$
assume this is used

 

[kaliprasad]

Calculate the sum for the infinite geometric series
$4+2+1+\frac{1}{2}+...$

all I know is the ratio is $\frac{1}{2}$

$\displaystyle\sum_{n}^{\infty}a{r}^{n}$
assume this is used

what is sum of Geometric series$\displaystyle\sum_{n= 0}^{\infty}a{r}^{n}= a (\frac{1}{1-r})$
using above
$= 4 (\frac{1}{1-\frac{1}{2}})= 4 * 2 = 8$

 

[karush]

Calculate the sum for the infinite geometric series
$4+2+1+\frac{1}{2}+...$

$a=4 \ \ r=\frac{1}{2}$

$\displaystyle\sum_{n= 0}^{\infty}a{r}^{n}= a (\frac{1}{1-r})
= 4 (\frac{1}{1-\frac{1}{2}})= 4 * 2 = 8$

 

[kaliprasad]

Calculate the sum for the infinite geometric series
$4+2+1+\frac{1}{2}+...$

$a=5 \ \ r=\frac{1}{2}$

$\displaystyle\sum_{n= 0}^{\infty}a{r}^{n}= a (\frac{1}{1-r})
= 4 (\frac{1}{1-\frac{1}{2}})= 4 * 2 = 8$

$a = 4$ and not 5

 

[karush]

Saw it, got it