[" 7.Let "R={(a,(1)/(a)):a in N" and "1

Let R={(a,(1)/(a)): A in N and 1 lt a lt 5}. Find the domain and range of R.

For x in(0,(pi)/(4)). Let S_(n)=sum_(r=1)^(2n)sin(sin^(-1)x^(3r-2)),C_(n)=sum_(r=1)^(2n)cos(cos^(-1)x^(3r-1)) and T_(n)=sum_(r=1)^(2n)tan(tan^(-1)x^(3r)) where n in N and n>=3

Let (1 + x)^(n) = sum_(r=0)^(n) a_(r) x^(r) . Then ( a+ (a_(1))/(a_(0))) (1 + (a_(2))/(a_(1)))…(1 + (a_(n))/(a_(n-1))) is equal to

Let S_(n)=sum_(r=1)^(oo)(1)/(n^(r)) and sum_(n=1)^(k)(n-1)S_(n)=5050, then k=

Let f(n), g (n) be polynomial in n and let Delta_(r)=|{:(r^(2).C_(r),n(n+1)2^(n-2),f(n)),(6r(n-r+1),n(n+1)(n+2),g(n)),(4(5^(r-1)),5^(n)-1,h(n)):}| , then evaluate underset(r=1)overset(n)sum Delta_(r) . (use (1+x)^(n)=underset(r=0)overset(n)sum(C_(r)x^(r)) )

Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest integer function, prove that Rf=4^(2n+1)

Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest integer function, prove that Rf=4^(2n+1)