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If S(1),S(2),S(3),"....",S(p) are the su...

If `S_(1),S_(2),S_(3),"....",S_(p)` are the sums of n terms of p AP's whose first terms are `1,2,3,"…",p` and common differences are `1,2,3,"…",(2p-1)` respectively, show that `S_(1)+S_(2)+S_(3)+"...."+S_(p)=(1)/(2)np(np+1).`

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