Question

Find the sum to
infinity
to the series : 16,-8, 4...​

Answer 1

Find the Sum of the Infinite Geometric Series 16 , 8 , 4 , 2. 16 16 , 8 8 , 4 4 , 2 2. This is a geometric sequence since there is a common ratio ...

Answer 2

Given:

$s=16-8+4+ \infty}$

To find:  

Sum of infinity to the series$(S\infty})$  

Formula:  

The sum of infinite geometric series ,  

          $S \infty} =\frac{a(1-r^{n}) }{1-r\\}$  

Geometric sequence:

$r=\frac{-8}{16} =\frac{4}{-8} =\frac{-1}{2}$

Therefore,  

$r =\frac{-1}{2}$

The values of $a=16$   and $r=\frac{-1}{2}$,can we put in the equation(S$\infty}$)

    $S \infty} =\frac{16}{1-(\frac{-1}{2}) }$

            $=\frac{16}{\frac{3}{2} }$

           $=\frac{32}{3}$

The sum of infinity to the series : $16,-8,4$ is  $\frac{32}{3}$