Answer :

Given the first k cubes of natural numbers and that their sum is 2025,

By formula we have S =


2025 =


Taking square root on both sides, we get = 45


k(k + 1) = 90


k2 + k = 90


Or k2 + k-90 = 0


Solving the quadratic using the quadratic formula



Where b = 1, a = 1, c = -90


We get,





k = is invalid because it yields a negative k which doesn’t make sense because number of terms in a series cannot be negative.


= 9


The sum S = 13 + 23 + 33 + … + k3 = 2025 corresponds to k = 9.


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