If S₁ and S₂ denote respectively the sum of first 100 natural numbers and the sum of their cubes, then the relation between S₁ and S₂ is __________.

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Solution

Let
S₁ : the sum of first 100 natural numbers
S₂ : the sum of their cubes.

$\begin{array}{rcl} S_{1} & = & \frac{n (n + 1)}{2} = \frac{100 (100 + 1)}{2} \\ S_{1} & = & 5050 \\ S_{2} & = & {(\frac{n (n + 1)}{2})}^{2} \\ = & {(\frac{100 (100 + 1)}{2})}^{2} \\ = & {(5050)}^{2} \\ S_{2} & = & {S_{1}}^{2} \end{array}$

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If S1 and S2 denote respectively the sum of first 100 natural numbers and the sum of their cubes, then the relation between S1 and S2 is __________.

Let S1 : the sum of first 100 natural numbers S2 : the sum of their cubes. S1= nn+12 = 100100+12S1= 5050S2= nn+122 = 100100+122 = 50502 S2= S12

If S₁ and S₂ denote respectively the sum of first 100 natural numbers and the sum of their cubes, then the relation between S₁ and S₂ is __________.