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