If `a_(n) = sin^(n) theta + cos^(n) theta` the P.T. `(a_(3) -a_(5))/(a_(1))=(a_(5)-a_(7))/(a_(3))`

a_(n) = 2^(n), a_(5) = ………

If a_(1), a_(2), a_(3), a_(4) are the coefficients of the 2^(nd), 3^(rd), 4^(th) and 5^(th) terms respectively in the binomial expansion of (1+x)^(n) where n is a positive integer prove that (a_(1))/(a_(1)+a_(2)) , (a_(2))/(a_(2)+a_(3)) , (a_(3))/(a_(3)+a_(4)) are in arithmetic progression.

If a_(n) = (n)/(n+1) , then a_(2017) = ………..

a_(n) = (n-1) (n-2) then a_(2) = ……….

If a_(1)Cos theta+b_(1) Sin theta+c_(1)=0 and a_(2) cos theta+ b_(2) sin theta +c_(2)= 0 then (b_(1)c_(2)-b_(2)c_(1))^(2)+(c_(1)a_(2)-c_(2)a_(1))^(2)=

a_(n) = n/(n+2) , a_(3) = ……….

If (a_(1) + ib_(1)) (a_(2) + ib_(2)) … (a_(n) + ib_(n)) = A + iB then Tan^(-1) ((b_(1))/(a_(1))) + Tan^(-1) ((b_(2))/(a_(2))) + …. + Tan^(-1) ((b_(n))/(a_(n))) =

If the coefficients of 4 consecutive terms in the expansion of (1+x)^(n) are a_(1),a_(2),a_(3),a_(4) respectively, then show that (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If a_(n) = (n(n+3))/(n+2) , then find a_(17) .

If a_(1), a_(2),….a_(n) are in H.P then (a_(1))/(a_(2) + a_(3) + …+ a_(n)), (a_(2))/(a_(1) + a_(3) + …+ a_(n)), (a_(3))/(a_(1) + a_(2) + a_(4)…+ a_(n)) ….(a_(n))/(a_(1) + a_(2) + a_(3) + ….a_(n-1))