Correct Answer - Option 3 : 3025

__Formula used:__

1 + 2 + 3 + ........ up to n term =

12 + 22+ 32+ ......up to n term = \(\frac{n(n\ +\ 1)(2n\ +\ 1)}{6}\)

13 + 23 + 33 + .....up to n term = \((\frac{n(n\ +\ 1)}{2})^2\)

__Calculation:__

Let,

S = 13 + 23 + 33 + ... + 103

We know that

13 + 23 + 33 + .....up to n term = \((\frac{n(n\ +\ 1)}{2})^2\)

Hence, the sum of given series is

S = \((\frac{10(10\ +\ 1)}{2})^2\)

⇒ S = 3025