Question

What is the convergent sum of the series?
Series is: 640, 320, 160, 80, 40.........

Answer 1

The sequence is geometric, since each term is the previous term multiplied by \(\frac{1}{2}\). The series is
\[ \sum_{n=0}^{\infty} 640\left(\frac{1}{2} \right)^n.\] You can find the sum to infinity of a geometric series using the formula
\[ \sum_{n=0}^{\infty} ar^n = \frac{a}{1-r}\] as long as -1<r<1. (In this case, a=640, and r=1/2.)

Answer 2

it is a G.P
a=640,r=320/640=1/2
\[S \infty =\frac{ a }{ 1-r }=\frac{ 640 }{1-\frac{ 1 }{ 2 } }=\frac{ 640 }{\frac{ 1 }{ 2 } }\]
=640*2=1280

Answer 3

Thanks guys.

Answer 4

yw