`(1)/(1)+(1)/(1+2)+(1)/(1+2+3)+.........2020` terms `=(m)/(n)` where `m, n` are coprime natural numbers then `(m)/(n-1)` is equal to
(1) `1`
(2)`2`
(3) `3`
(4) None of these

If sum_(i=1)^(10)tan^(-1)((3)/(9r^(2)+3r-1))=cot^(-1)((m)/(n)) (where m and n are coprime) then the value of (2m+n)/(8) is

(tan^(-1)((1)/(3))+tan^(-1)((1)/(7))+tan^(-1)((1)/(13))+......+tan^(-1)((1)/(381)))=(m)/(n) where m,n in N, then find least value of (m+n)

If theta=tan^(-1)((1)/(10))+tan^(-1)((1)/(9))+...+tan^(-1)(1)+tan^(-1)(2)+...+tan^(-1)(10)+tan^(-1)(11) .If tan theta=(m)/(n) (where m,n are coprime) then the value of (m+n) is equal to

f(1)=1 and f(n)=2sum_(r=1)^(n-1)f(r). Then sum_(n=1)^(m)f(n) is equal to (A)3^(m)-1(B)3^(m)(C)3^(m-1) (D)none of these

" The value of "cot^(-1)((1+2^(2))/(3))+cot^(1)((1+6^(2))/(5))+cot^(-1)((1+12^(2))/(7))+..." up to "8" terms is "tan^(-1)((m)/(n))" .(where "m,n" are coprime ) then "m+n" is equal to "

(1)/(1*2)+(1)/(2*3)+(1)/(3*4)+"…."+(1)/(n(n+1)) equals

The number of all pairs (m, n), where m and n are positive integers, such that 1/(m)+1/(n)+1/(mn)=2/(5) is