Find the value of k if

1³ + 2³ + 3³ + … + k³ = 2025

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.