Question

Express the series using sigma notation. 1 + 4 + 16 + ... + 256.

Answer 1

Choice (D)

Explanation:

The series is exponential, so only (C) and (D) are candidates. The first element of the series is 1, which is produced by 4^0, so k must include 0. This matches choice (D), and excludes choice (C).

Answer 2

D) is the correct option .

Explanation:

Given : 1 + 4 + 16 + ... + 256.

To find : Express the series using sigma notation.

Solution : We have given that

1 + 4 + 16 + ... + 256.

We can see the relation between the numbers in series.

`4^(0)  = 1\\4^(1)  = 4\\4^(2)  = 16........4^(4)  = 256`

So we can write the series as
`4^(k)`.

But value of k lies from 0 to 4.

Then Sum :
`4^(0) + 4^(1)  + 4^(2) +........+4^(4)`.

Therefore, D) is the correct option .