Question

Use the formula to evaluate the series 1+2+4+8+...a10

Answer 1

Answer:

The sum of the given series is 1023

Step-by-step explanation:

Geometric series states that a series in which a constant ratio is obtained by multiplying the previous term.

Sum of the geometric series is given by:

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

where a is the first term and n is the number of term.

Given the series: $1+2+4+8+.................+a_{10}$

This is a geometric series with common ratio(r) = 2

We have to find the sum of the series for 10th term.

⇒ n = 10 and a = 1

then;

$S_n = \frac{1(1-2^{10})}{1-2} =\frac{1-1024}{-1} =\frac{-1023}{-1}=1023$

Therefore, the sum of the given series is 1023