Question

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

Answer 1

The correct answer is 13.75

Explanation:

4+2= 6

6+1=7

6+7= 13

13+1/2= 13.5

13.5+1/4= 13.75

Answer 2

`s_10=(1023)/(128)`

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((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((1-((1)/(2))^n))/(1-((1)/(2)))`

Given n=10

`s_10= 4((1-((1)/(2))^(10)))/(1-((1)/(2)))=(1023)/(128)`