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Q.

The value of $(1^{3} + 2^{3} + \dots + 20^{3}) - (1 + 2 + 3 + \dots + 20)$ is given by

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a

48890

b

45890

c

43890

d

47890

answer is D.

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Detailed Solution

Σ n^{3} = \frac{n^{2} {(n + 1)}^{2}}{4}

$Σ n^{3} = \frac{20^{2} {(20 + 1)}^{2}}{4} = \frac{400 \times 441}{4} = 44100 (∵ n = 20)$

$Σ n = \frac{n (n + 1)}{2} = \frac{20 \times 21}{2} = 210$

$= 44100 - 210 = 43890$

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