Question

Evaluate the series 4+2+1+1/2+1/4 to s10

Answer 1

Answer:

The correct answer is 13.75

Step-by-step explanation:

4+2= 6

6+1=7

6+7= 13

13+1/2= 13.5

13.5+1/4= 13.75

Answer 2

Answer:

$s_10=\frac{1023}{128}$

Step-by-step explanation:

4+2+1+1/2+1/4.....

WE need to find out the sum s10

first term is 4 and second term is 2

2/4 = 1/2

1/2= 1/2

1/2 / 1= 1/2

so common ratio is 1/2

The given series is geometric series

we use the sum formula for the geometric series

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

Where 'r' is the common ratio and 'a' is the first term

a= 4  and r= 1/2

Plug in the values in the sum formula'

$s_n= 4\frac{(1-(\frac{1}{2})^n)}{1-(\frac{1}{2})}$

Given n=10

$s_10= 4\frac{(1-(\frac{1}{2})^{10})}{1-(\frac{1}{2})}=\frac{1023}{128}$