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If Sn be the sum of n consecutive terms of an A.P. show that `S_(n+4)-4S_(n+3)+6S_(n+2)-4S_(n+1)+S_n=0`

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If S_(n) be the sum of n consecutive terms of an A.P. show that, S_(n+4) - 4S_(n+3) + 6S_(n+2) -4S_(n+1) +S_(n) = 0

If S_(n) be the sum of n consecutive terms of an A.P. show that, S_(n+3) - 3S_(n+2) + 3S_(n+1) - S_(n) = 0

If S_n be the sum of the n consecutive terms of an A.P,find the value of S_(n+3)-3S_(n+2)+3S_(n+1)-Sn

If S_(1), S_(2), S_(3) be respectively the sums of n, 2n and 3n terms of a G.P., prove that, S_(1)(S_(3) - S_(2)) = (S_(2) - S_(1))^(2) .

If S_1,S_2 and S_3 be respectively the sum of n, 2n and 3n terms of a G.P., prove that S_1(S_3-S_2)=((S_2)-(S_1))^2

Let S_n denote the sum of first n terms of an A.P. If S_(2n)=3S_n , then find the ratio S_(3n)//S_ndot

If the sum of 1st n tenn of a GP is S_n=1 and S_(2n)=4 ,show that S_(3n):S_n=13:1

Let S_(n) be the sum of first n terms of an A.P. If S_(2n) = 5s_(n) , then find the value of S_(3n) : S_(2n) .

If S_1, S_2 and S_3 be respectively the sum of n, 2n and 3n terms of a G.P .Prove that S_1(S_3-S_2)=(S_2-S_1)^2 .

If S_(n) be the sum of first n terms of a G.P. whose common ratio is r, then show that, (r-1)(dS_(n))/(dr)=(n-1)S_(n)-nS_(n-1)

UNITED BOOK HOUSE-MCQ-EXERCISE
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