[" किसी समान्तर श्रेढी में "(S_(m))/(S_(n))=(m^(4))/(n^(4))" तो सिद्ध कीजिए "],[qquad (T_(m+1))/(T_(n+1))=((2m+1)^(3))/((2n+1)^(3))]

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. 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 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)

Let T_(r) and S_(r) be the rth term and sum up to rth term of a series,respectively.If for an odd number n,S_(n)=n and T_(n)=(T_(n)-1)/(n^(2)), then T_(m)(m being even) is (2)/(1+m^(2)) b.(2m^(2))/(1+m^(2)) c.((m+1)^(2))/(2+(m+1)^(2))d(2(m+1)^(2))/(1+(m+1)^(2))

Let S_(n) and Delta_(n) be the sum of first n terms of 2A.P' 's whose r_(th) term are T_(r) and t_(r) respectively.If (S_(n))/(Delta_(n))=(2n+5)/(3n+2) then (T_(11))/(t_(10))=(m_(1))/(m_(2)) where m_(1) and m_(2) are coprime. Find the value of (m_(2)-m_(1))/(2) = ?

Let S_(n) and Delta_(n) be the sum of first n terms of 2 A. P' s whose rth term are T_(r) and t_(r) respectively.If (S_(n))/(Delta_(n))=(2n+5)/(3n+2) then (T_(11))/(t_(11))=(m_(1))/(m_(2)) where m_(1) and m_(2) are coprime. Find the value of (m_(2)-m_(1))/(2)=

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}