Question

What will come in place of question mark (?) in the following question?

(1³ + 2³ + 3³ + ……………. + 30³) – (1² + 2² + 3² + ………………+ 30²) = ?

1. 2366770
2. 246770
3. 206770
4. 286770
5. 226770

Answer 1

Correct Answer - Option 3 : 206770

Given:

(1³ + 2³ + 3³ + ……………. + 30³) – (1² + 2² + 3² + ………………+ 30²)

Formula used:

1² + 2² + 3² + ……………. + n² = [n(n + 1)(2n + 1)]/6

1³ + 2³ + 3³ + ……………. + n³ = [n(n + 1)/2]³

Calculation:

Let a = 1³ + 2³ + 3³ + ………….. + 30³   

And b = 1² + 2² + 3³ + ……………. + 30²

a = 1³ + 2³ + 3³ + …………... + 30³

Here n = 30

⇒ [n(n + 1)/2]²

⇒ [30 (30 + 1)/2]²

⇒ (15 × 31)²

⇒ 216225

b = 1² + 2² + 3² + …………….. + 30²

Here n = 30

⇒ [n(n + 1)(2n + 1)]/6

⇒ [30(30 + 1)(2 × 30 + 1)]/6

⇒ (5 × 31 × 61)

⇒ 9455

Then, a – b = 216225 – 9455 = 206770

∴ The value of ‘?’ is 206770.