The correct option is A 2989 We know that, ∑_k=1^nk^3=n^2(n+1)^24 ∑_k=1^10k^3=10^2(10+1)^24=3025 ∑_k=1^3k^3=3^2(3+1)^24=36 The given questio ...

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Question

$4^{3} + 5^{3} + 6^{3} + \dots . . + 10^{3} =$

1905

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Solution

The correct option is A $2989$
We know that,
$\sum_{k = 1}^{n} k^{3} = \frac{n^{2} (n + 1)^{2}}{4}$
$\sum_{k = 1}^{10} k^{3} = \frac{10^{2} (10 + 1)^{2}}{4} = 3025$
$\sum_{k = 1}^{3} k^{3} = \frac{3^{2} (3 + 1)^{2}}{4} = 36$
The given question is,
$\sum_{k = 1}^{10} k^{3} - \sum_{k = 1}^{3} k^{3} = 3025 - 36 = 2989$
Hence, option 'D' is correct.

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