The sum 11^3 + 12^3 + dots + 20^3 is: | vedclass

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Question

(B) The sum is given by $S = \sum_{n=11}^{20} n^3 = \sum_{n=1}^{20} n^3 - \sum_{n=1}^{10} n^3$. Using the formula $\sum_{k=1}^{n} k^3 = \left[ \frac{n

Vedclass · Accepted Answer

An odd integer divisible by $5$.

Vedclass · Answer

(B) The sum is given by $S = \sum_{n=11}^{20} n^3 = \sum_{n=1}^{20} n^3 - \sum_{n=1}^{10} n^3$. Using the formula $\sum_{k=1}^{n} k^3 = \left[ \frac{n(n+1)}{2} \right]^2$: $S = \left[ \frac{20(21)}{2} \right]^2 - \left[ \frac{10(11)}{2} \right]^2$ $S = (210)^2 - (55)^2$ $S = 44100 - 3025 = 41075$. Since the number $41075$ ends in $5$,it is divisible by $5$. Since it is not divisible by $2$,it is an odd integer. Therefore,the sum is an odd integer divisible by $5$.

The sum $11^3 + 12^3 + \dots + 20^3$ is:

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