Q. 2 B

# Find the value of k if13 + 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

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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