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If S1,S2,.....So are the sum of n terms of AP whose first terms are 1,2,... P and the common difference are 1,3,5,......(2p-1) respectively then S1+S2+.....+Sp=

If S1,S2,.....So are the sum of n terms of AP whose first terms are 1,2,... P and the common difference are 1,3,5,......(2p-1) respectively then S1+S2+.....+Sp=

Grade:11

1 Answers

Aditya Gupta
2081 Points
3 years ago
we see that Sk= n/2*[2k + (n – 1)*(2k – 1)]
now, S1+S2+.....+Sp= n/2*∑2kn+1-n
=n/2*(∑2kn+∑1-n)
now using the fact that ∑k=p(p+1)/2 and then simplifying, we get
 S1+S2+.....+Sp= np(np+1)/2

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