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What is the sum of the cubes of the natural numbers from 5 to 14?
Question

What is the sum of the cubes of the natural numbers from 5 to 14?

A.

10920

B.

10925

C.

10930

D.

10935

Correct option is B

Given:
The numbers are: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.
Formula Used:
Sum of cubes from 1 to n:
(n(n+1)2)2\left( \frac{n(n+1)}{2} \right)^2​​
Solution:
Sum of cubes from 1 to 14:
S14=(14(14+1)2)2=(14×152)2=1052=11025S_{14} = \left( \frac{14(14+1)}{2} \right)^2 = \left( \frac{14 \times 15}{2} \right)^2 = 105^2 = 11025​​
Sum of cubes from 1 to 4:
S4=(4(4+1)2)2=(4×52)2=102=100S_4 = \left( \frac{4(4+1)}{2} \right)^2 = \left( \frac{4 \times 5}{2} \right)^2 = 10^2 = 100​​
Now,
S(5 to 14) = 11025 − 100 = 10925

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