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given an AP whose sum of n terms is n2p and same AP with m terms whose sum is m2p

To prove: Sp = p3

we know that the sum of AP is given by the formula: substituting the values in the above equation, we get …. (i)

Similarly, for series with m terms …(ii)

Subtracting (ii) from (i) we get

d = 2p

substituting d in (i) we get

a = p

Now using the sum formula for AP consisting of p terms we get Substituting the values in the above equation SP = p3

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