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

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1 Answer

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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

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

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