Find the value of k if

1³ + 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

Solving the quadratic using the quadratic formula

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.