If `S_n = sum_(r=1)^n \ (2r+1)/(r^4+2r^3+r^2)`, then `S_10` is equal to

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

lim_(n->oo) sum_(r=1)^ntan^(- 1)((2r+1)/(r^4+2r^3+r^2+1)) is equal to

If S_(n) = sum_(r=1)^(n) (r )/(1.3.5.7"……"(2r+1)) , then

sum_(r=1)^( If )(r^(2)+3r+3)(r+1)!=998(998!)-4 then n is equal to

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