# Sum of finite series given sum of cubes [closed]

The question says - If $1^3+2^3+3^3+\cdots+10^3=3025$, then what is the value of the following series which is ?

$$4+32+108+\cdots+4000$$

## closed as off-topic by Sahiba Arora, Simply Beautiful Art, Dando18, user223391, Ian MillerAug 11 '17 at 15:11

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• Hint:$$4=4\times1^3\\32=4\times2^3\\108=4\times3^3\\\vdots$$ – Simply Beautiful Art Aug 11 '17 at 14:36

Answer is $12100$
Solution $-$ \begin{eqnarray*} 4 + 32 + 108 + \cdots + 4000 &=& 4 (1 + 8 + 27 + ….. 1000) \\ &=& 4 (1^3 + 2^3 + 3^3 + \cdots + 10^3 )\\ &=& 4 \times 3025 = \color{blue}{12100} \ (\text{Answer}) \end{eqnarray*} Go to http://jobsandhan.com/mcq-questions-answers/arithmetic-aptitude/ Question No $11$ and check solution
• Great first answer. $\ddot \smile$ – Donald Splutterwit Aug 11 '17 at 14:46