Suppose a1, a2,... are in AP and Sk, den...

Suppose `a_1, a_2,...` are in AP and `S_k`, denotes the sum of the first `k` terms of this AP. If `S_n/S_m = n^4/m^4` for all `m, n in NN`, then prove that `a_(m+1)/a_(n+1) = (2m+1)^3/(2n+1)^3`

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Suppose a_(1),a_(2),... are in AP and S_(k), denotes the sum of the first k terms of this AP.If (S_(n))/(S_(m))=(n^(4))/(m^(4)) for all m,n in N, then prove that (a_(m+1))/(a_(n+1))=((2m+1)^(3))/((2n+1)^(3))

If S_(n) denotes the sum of first n terms of an A.P., then (S_(3n)-S_(n-1))/(S_(2n)-S_(n-1)) is equal to

If S_n denotes the sum of first n terms of an A.P. such that (S_m)/(S_n)=(m^2)/(n^2), t h e n(a_m)/(a_n)= a.(2m+1)/(2n+1) b. (2m-1)/(2n-1) c. (m-1)/(n-1) d. (m+1)/(n+1)

If S_(n) denotes the sum of first n terms of an AP, then prove that S_(12)=3(S_(8)-S_(4)).

If S_(1) be the sum of (2n+1) term of an A.P. and S_(2) be the sum of its odd terms then prove that S_(1):S_(2)=(2n+1):(n+1)

In an A.P., S_(m) = n and S_(n) = m also m gt n ,find the sum of first (m-n) terms .

In an A.P.the sum of m terms of an AP is n and sum of n terms of AP is m,then prove that sum of (m+n) terms of AP is -(m+n)

If S_(m)=m^(2) p and S_(n)=n^(2)p , where m ne n in an AP then prove that S_(p) =P^(3)

If in an A.P., S_n=n^2p and S_m=m^2p , where S_r denotes the sum of r terms of the A.P., then S_p is equal to 1/2p^3 (b) m n\ p (c) p^3 (d) (m+n)p^2

The ratio of the sums of m terms and n terms of an A.P. is m^(2) : n^(2). Prove that the ratio of their mth and nth term will be (2m - 1) : (2n-1).

MOTION-SEQUENCE & SERIES -Exercise -4 Level -II Previous Year /JEE Advanced

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