Given that the series S = 1 + 2 + 3 + … + p = 171
We have S = \(\frac{p(p+1)}{2}\) = 171
p(p + 1) = 342
p2 + p = 342
Or p2 + p-342 = 0
Solving the quadratic using the quadratic formula
p = \(\frac{-1-37}{2}\)is invalid because it yields a negative p which doesn’t make sense because number of terms in a series cannot be negative.
p = \(\frac{-1+37}{2}\) = 18
S = 13 + 23 + 33 + ... + p3 where p = 18
Formula to find the sum of first n cubes of natural numbers is
The sum S = 13 + 23 + 33 + ... + p3 corresponds to p = 18 and S = 29241.