[" Determine the radius of convergence of "],[" 1."sum_(m=0)^(oo)(1)/(2^(m))(x-1)^(2m)]

Interval of convergence of the power series sum_(k=1)^(oo)((x+2)^(k))/(k sqrt(k+1)) is

sum_(m=1)^(oo)Tan^(-1) ((2m)/(m^(4)+m^(2)+2))=

The value of sum_(m=1)^(oo)tan^(-1)((2m)/(m^(4)+m^(2)+2)) is

The value of sum_(m=1)^ootan^(- 1)((2m)/(m^4+m^2+2)) is

The value of sum_(m=1)^ootan^(- 1)((2m)/(m^4+m^2+2)) is

Let m,n be two positive real numbers and define f(n)=int_(0)^(oo)x^(n-1)e^(-x)dx and g(m,n)=int_(0)^(1)x^(m-1)(1-m)^(n-1)dx . It is known that f(n) for n gt 0 is finite and g(m, n) = g(n, m) for m, n gt 0. int_(0)^(oo)(x^(m-1))/((1+x)^(m+n))dx=

Find the value of sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p)) And hence,find the value of lim_(n rarr oo)(1)/(3^(n))sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p))

If M is the matrix [(1,-3),(-1,1)] then find matrix sum_(r=0)^(oo) ((-1)/3)^(r) M^(r+1)

If M is the matrix [(1,-3),(-1,1)] then find matrix sum_(r=0)^(oo) ((-1)/3)^(r) M^(r+1)