Answer :

Given that the series S = 13 + 23 + 33 + … + k3 = 8281


Formula to find the sum of first k cubes of natural numbers is


S =


8281 =


Taking square root on both sides,


91 =


k(k + 1) = 182


k2 + k = 182


Or k2 + k-182 = 0


Solving the quadratic using the quadratic formula



Where b = 1, a = 1, c = -182


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.


= 13


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


Given series 1 + 2 + 3…. + k, we have k = 13


We have S =


=


=


S = 91


The sum S = 13 + 23 + 33 + ... + k3 corresponds to k = 13 and 1 + 2 + 3…. + k = 91.


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