Question

Find the value of (1^3+2^3+3^3..........15^3)-(1+2+3.....15)

Answer 1

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Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

As we can see it is in the form of

$\Sigma {n}^{3} - \Sigma{n}$

So, by putting the respective formula we get,

$\implies \: \Sigma {n}^{3} - \Sigma{n}$

$\sf{\implies \: [{ \frac{n(n + 1)}{2}]}^{2}- \frac{n(n + 1)}{2} }$

$\sf{ \implies \: [{ \frac{15(15+ 1)}{2}]}^{2}- \frac{15(15 + 1)}{2} }$

$\sf{ \implies \: [{ \frac{15(16)}{2}]}^{2}- \frac{15(16)}{2} }$

$\sf{ \implies \: [{ \frac{240}{2}]}^{2}- \frac{240}{2} }$

$\sf{ \implies \: {(120)}^{2}- 120}$

$\sf{ \implies \: 14400- 120}$

$\sf{ \implies \: 14280}$

$\boxed{ \sf{Hence, \: our \: required \: value \: is \: 14280}}$