Question

If 1³ + 2³ + 3³ + 4³ +... + 7³ = 784, then the value of (0.2)³ + (0.4)³ + (0.6)³ + (0.8)³ + ... + (1.4)³ is
1. 5.272
2. 6.272
3. 6.274
4. 6.476

Answer 1

Correct Answer - Option 2 : 6.272

Given:

13 + 23 + 33 + 43 +... + 73 = 784

Calculation:

(0.2)3 + (0.4)3 + (0.6)3 + (0.8)3 + ... + (1.4)3 

= 10^-3 ( 2³ + 4³ + 6³ + 8³ + ............+ 14³ )

= 10-3 ( 2³ × 1³ + 23 × 23 + 23 × 33 + 23 × 43 + .......................+ 23 × 73 )

= 10-3 × 2³ ( 13 + 23 + 33 + 43 + .......................+ 73 )

Using given result, we get as

= 10-3 × 23 ( 784 )

= 6.272