Find the sum of the series.
$1^{3} + 2^{3} + 3^{3} + .... + 2 0^{3}$

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Find the sum of the series.

1^{3} + 2^{3} + 3^{3} + .... + 2 0^{3}

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Text solutionVerified

We know

1^{3} + 2^{3} + 3^{3} + .... + 2 0^{3} = 1 \sum 20 n^{3}

= (\frac{20 ( 20 + 1 )}{2})^{2}

using

k = 1 \sum n k^{3} = [\frac{n ( n + 1 )}{2}]^{2}

= (\frac{20 \times 21}{2})^{2} = (210)^{2} = 44100

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