If 1 + 2 + 3 + … + p = 171, then find 1³ + 2³ + 3³ + ... + p³.

Given that the series S = 1 + 2 + 3 + … + p = 171

We have S =

p(p + 1) = 342

p² + p = 342

Or p² + p-342 = 0

Solving the quadratic using the quadratic formula

Where b = 1, a = 1, c = -342

We get,

p = is invalid because it yields a negative p which doesn’t make sense because number of terms in a series cannot be negative.

= 18

S = 1³ + 2³ + 3³ + ... + p³ where p = 18

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

S =

S =

S =

S = 29241

The sum S = 1³ + 2³ + 3³ + ... + p³ corresponds to p = 18 and S = 29241.