" If "a_(n)=(n)/((n+1)!)," then find "sum_(n=1)^(50)a_(n)

If alpha,beta are the roots of equation x^(2)-10x+2=0 and a_(n)=alpha^(n)-beta^(n) then sum_(n=1)^(50)n.((a_(n+1)+2a_(n-1))/(a_(n))) is more than (a)12500 (b)12250 (c)12750 (d)12000

For a sequence {a_(n)},a_(1)=2 and (a_(n+1))/(a_(n))=(1)/(3) then sum_(r=1)^(20)a_(r) is

For a sequence a_(n),a_(1)=2 If (a_(n+1))/(a_(n))=(1)/(3) then find the value of sum_(r=1)^(oo)a_(r)

For a sequence {a_(n)}, a_(1) = 2 and (a_(n+1))/(a_(n)) = 1/3 , Then sum_(r=1)^(oo) a_(r) is

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

Let a_(1),a_(2),......a_(n) be real numbers such that sqrt(a_(1))+sqrt(a_(2)-1)+sqrt(a_(3)-2)++sqrt(a_(n)-(n-1))=(1)/(2)(a_(1)+a_(2)+......+a_(n))-(n(n-3)/(4) then find the value of sum_(i=1)^(100)a_(i)

A sequence of numbers A_(n)n=1,2,3... is defined as follows: A_(1)=(1)/(2) and for each n>=2,A_(n)=((2n-3)/(2n))A_(n-1), then prove that sum_(k=1)^(n)A_(k) =1

If S_(n)=sum_(r=1)^(n) a_(r)=(1)/(6)n(2n^(2)+9n+13) , then sum_(r=1)^(n)sqrt(a_(r)) equals

The Fibonacci sequence is defined by 1=a_(1)=a_(2) and a_(n)=a_(n-1)+a_(n-2),n>2 Find (a_(n+1))/(a_(n)),f or n=5