Answer:
D) is the correct option .
Step-by-step 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.
[tex]4^{0} = 1\\4^{1} = 4\\4^{2} = 16........4^{4} = 256[/tex]
So we can write the series as [tex]4^{k}[/tex].
But value of k lies from 0 to 4.
Then Sum : [tex]4^{0} + 4^{1} + 4^{2} +........+4^{4}[/tex].
Therefore, D) is the correct option .
