Question

The value of (1³ + 2³ + 3³ + ........+15³) - (1+2+3+.........+15) is

• A. 14280
• B. 14400
• C. 12280
• D. 13280

Answer 1

The Correct Option is A

Let's Assume the sum of \(n\) consecutive natural number cubes be \([\frac{n(n + 1)}{2}]^2\)

The sum of \(n\) consecutive natural numbers be \(\frac{n(n + 1)}{2}\)

The Expression given = \((1^3 + 2^3 + 3^3 + ......... + 15^3)\) - \((1 + 2 + 3 + ......... + 15)\)

= From the above = \([ \frac{15(15 + 1)}{2}]^2 - \frac{15 × 16}{2}\)

= \([\frac{15 × 16}{2}]^2 - \frac{15 × 16}{2}\)

= \((120)^2\) - 120

= 14400 - 120

= 14280 

The correct option is (A): 14280