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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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