11^3 + 12^3 + .... + 20^3 - Vidyadip

MCQ

${11^3} + {12^3} + .... + {20^3}$

A
Is divisible by $5$
✓
Is an odd integer divisible by $5$
C
Is an even integer which is not divisible by $5$
D
Is an odd integer which is not divisible by $5$

✓

Answer

Correct option: B.

Is an odd integer divisible by $5$

b
(b) $\sum\limits_{n = 1}^{20} {({n^3})} - \sum\limits_{n = 1}^{10} {({n^3})} $

$= \left[ {\frac{{n(n + 1)}}{2}} \right]_{n = 20}^2 - \left[ {\frac{{n(n + 1)}}{2}} \right]_{n = 10}^2$

$= 44100 -3025 = 41075.$

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