If `S_n=sum_(r=1)^n(1+2+2^2+ .......+2^r)/(2^r),` then `S_n` is equal to (a)`2^n n-1` (b) `1-1/(2^n)` (c) 2n`-1+1/(2^n)` (d) `2^n-1`

If S_n=sum_(r=1)^n(1+2+2^2+ .......+2^r)/(2^r), then S_n is equal to (a) 2^n n-1 (b) 1-1/(2^n) (c) n -1+1/(2^n) (d) 2^n-1

if S_(n)=sum_(r=1)^(n)(1+2+2^(2)......... rterms )/(2^(r)) then S_(n) is equal to

If S_(n)=sum_(r=1)^(n)(1+2+2^(2)+2^(3)+.... rterms )/(2^(r)) then S_(-)n is equal to

If S_(n)=sum_(r=1)^(n)(2r+1)/(r^(4)+2r^(3)+r^(2)), then S_(10) is equal to

sum_(r=1)^(n) tan^(-1)(2^(r-1)/(1+2^(2r-1))) is equal to a) tan^(-1)(2^n) b) tan^(-1)(2)^n-pi/4 c) tan^(-1)(2^(n+1)) d) tan^(-1)(2^(n+1))-pi/4

If sum_(r=0)^(2n)a_(r)(x-100)^(r)=sum_(r=0)^(2n)br(x-101)^(r) and a_(k)=(2^(k))/(kC_(n))AA k>=n then b_(-) n equals ( A )2^(n)(2^(n+1)-1)(B)2^(n)(2^(n)-1)(C)2^(n)(2^(n)+1)(D)2^(n+1)(2^(n)-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

If (1-x^(2))^(n)=sum_(r=0)^(n)a_(r)x^(r)(1-x)^(2n-r), then a_(r) is equal to ^(n)C_(r) b.^(n)C_(r)3^(r) c.^(2n)C_(r) d.^(n)C_(r)2^(r)