Question

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

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

Answer 1

Answer: (A)

14280

Answer 2

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