`sum_(i=1)^ootan^(- 1)(1/(2i^2))=t ,t h e n t a nt=( B )1/2`

sum_(i=1)^(oo)tan^(-1)((1)/(2i^(2)))=t, thentant =(B)(1)/(2)

The sum sum _(n=1)^ootan^(-1)(1/(2^n+2^(1-n))) equals

Let s_(1), s_(2), s_(3).... and t_(1), t_(2), t_(3) .... are two arithmetic sequences such that s_(1) = t_(1) != 0, s_(2) = 2t_(2) and sum_(i=1)^(10) s_(i) = sum_(i=1)^(15) t_(i) . Then the value of (s_(2) -s_(1))/(t_(2) - t_(1)) is

Let s_(1),s_(2),s_(3),... and t_(1),t_(2),t_(3)... are two arithmetic sequences such that s_(1)=t_(1)!=0,s_(2)=2t_(2) and sum_(i=1)^(10)s_(1)=sum_(i=1)^(15)t_(1) Then the value of (s_(2)-s_(1))/(t_(2)-t_(1)) is

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

If sum_(r=1)^(n)t_(r)=(1)/(4)n(n+1)(n+2)(n+3) then value of (1)/(sum_(r=1)^(oo)((1)/(t_(r)))) is

If I_(1)=int_(x)^(1)(1)/(1+t^(2))dt and I_(2)=int_(1)^((1)/(2))(1)/(1+t^(2))dt for x>=0 then (A) I_(1)=I_(2)(B)I_(1)>I_(2)(C)I_(1)