Question

how many term of series 1+2+2^2+....must be taken to make 511

Answer 1

Answer:

16

Step-by-step explanation:

Given : $1+2+2^2+....$

To Find : how many term of series $1+2+2^2+....$  must be taken to make 511.

Solution:

G.P. : $1+2+2^2+....$

r = common ratio = $\frac{2}{1} = \frac{2^2}{2} =2$

First term a = 1

Sum of n terms in G.P. = $a \frac{1-r^n}{1-r}$

So, $511 = 1\frac{1-2^n}{1-2}$

$511 =2n^2-1$

$512=2n^2$

$256=n^2$

$16=n$

Hence 16 terms of series$1+2+2^2+....$   must be taken to make 511