Question

What is the sum of this geometric series?

Answer 1

I think D

Explanation:

Answer 2

D

Explanation:

`\sum\limits_(k=1)^38((1)/(4))^(k-1)`

The symbol '
`\sum`' , read as sigma, is the symbol for summation. Since the expression below sigma is 'k= 1', while the number above sigma is 3, we are to find the sum of
`8((1)/(4))^(k-1)` with each other from k =1 to k =3.

`\boxed{\text{Multiple rule}: \sum\limits_(i=1)^nku_i=k\sum\limits_(i=1)^nu_i}`

`\sum\limits_(k=1)^38((1)/(4))^(k-1)`

=
`8\sum\limits_(k=1)^3((1)/(4))^(k-1)` (Applying multiple rule)

=
`8[((1)/(4))^(1-1)+((1)/(4))^(2-1)+((1)/(4))^(3-1)]`

=
`8[((1)/(4))^0+((1)/(4))^1+((1)/(4))^2]`

=
`8(1+(1)/(4)+(1)/(16))`

=
`8((21)/(16))`

=
`\bf{(21)/(2) }`

Thus, the answer is D.