Q. 35.0( 1 Vote )

# 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

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.

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