Q. 2 A4.5( 2 Votes )

# Find the value of k if13 + 23 + 33 + … + k3 = 6084

Given the first k cubes of natural numbers and that their sum is 6084,

By formula we have S = 6084 = Taking square root on both sides, we get = 78

k(k + 1) = 156

k2 + k = 156

Or k2 + k-156 = 0 Where b = 1, a = 1, c = -156

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. = 12 The sum S = 13 + 23 + 33 + … + k3 = 6084 corresponds to k = 12.

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