Question

Choose the correct answer form the alternatives given.
$1^3+2^3+3^3+4^3+\cdots +{15}^3$ = ?

• A. 11025
• B. 13400
• C. 900
• D. 14400`

Answer 1

The correct option is D 14400`

$1^3 \, + \, 2^3 \, + \, 3^3 \, + \, \cdots \, + \, 15^3$

$[\therefore 1^3+2^3+\cdots +x^3={\left\{\frac{x(x+1)}{2}\right\}}^2]$

$= \left [ \frac{15 \, \times \, 16}{2} \right ]^2 \, = \, (120)^2 \, = \, 14400 $