Question

Find the sum of the series 1 + 4 + 9 +16 + 25 + 36 +......+ 121 ?
1. 506
2. 523
3. 525
4. None of these

Answer 1

Correct Answer - Option 1 : 506

Concept:​

• 1² + 2² + 3² + ..... + n² = \(\frac{n(n+1)(2n+1)}{6}\)

Calculation:

Here we have to find the sum of the series 1 + 4 + 9 +16 + 25 + 36 +......+ 121

The given series can be re-written as: 1² + 2² + 3² + ..... + 11²

As we know that, 12 + 22 + 32 + ..... + n2 = \(\frac{n(n+1)(2n+1)}{6}\)

Here, n = 11

⇒ 12 + 22 + 32 + ..... + 11² = \(\frac{11 \times 12 \times 23}{6} = 506\)

Hence, option 1 is the correct answer.