" If "a_(n)=n(n!)," then "sum_(r=1)^(100)a_(r)" is equal to "

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

If a_(n)=sum_(r=0)^(n)(1)/(""^(n)C_(r)) then sum_(r=0)^(n)(r)/(""^(n)C_(r)) equal to

For a sequence, if a_(1)=2 and (a_(n+1))/(a_(n))=(1)/(3). Then, sum_(r=1)^(20) a_(r) is

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

Let a_(n) be the nth term of an A.P. If sum_(r=1)^(100) a_(2r) = alpha and sum_(r = 1)^(100) a_(2r-1) = beta , then the common difference of the A.P. is :

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 (1-x)^(-n)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(r)x^(r)+..., then a_(0)+a_(1)+a_(2)+...+a_(r) is equal to (n(n+1)(n+2)...(n+r))/(r!)((n+1)(n+2)...(n+r))/(r!)(n(n+1)(n+2)...(n+r-1))/(r!) none of these

If a_(n)=sum_(r=0)^(n)(1)/(nC_(r)), then sum_(r=0)^(n)(r)/(nC_(r)) equals

Let a_(n) be the nth term of an AP, if sum_(r=1)^(100)a_(2r)= alpha " and "sum_(r=1)^(100)a_(2r-1)=beta , then the common difference of the AP is