Question

What is the value of S4 for
A. 5 5/64
B. 5 1/4
C. 5 5/16
D. 5 5/6

Answer 1

Answer: Option 'C' is correct.

Explanation:

Answer 2

Answer: Option 'C' is correct.

Explanation:

Since we have given that

`S_n=\sum^(\infty)_(n=1)4((1)/(4))^(n-1)`

We need to find the value of S₄.

So, it means sum of 4 terms.

Here it form a geometric series:

a = 4 = first term

r =
`(1)/(4)` = Common ratio

And sum of n terms whose ratio is less than 1 is given by

`S_n=(a(1-r^n))/(1-r)\\\\S_4=(4(1-(1)/(4)^(4)))/(1-(1)/(4))\\\\S_4=(4(1-0.25^4))/(1-0.25)\\\\S_4=(4(1-0.0039))/(0.75)\\\\S_4=5.3125\\\\S_4=5(5)/(16)`

Hence, Option 'C' is correct.