Prove that `ta n^-1 1/3 + ta n ^-1 1/5 + ta n ^-1 1/7 + ta n ^-1 1/8 = pi/4`

Prove that tan ^ (- 1) ((1) / (3)) + tan ^ (- 1) ((1) / (7)) + tan ^ (- 1) ((1) / (13)) + ......... + tan ^ (- 1) ((1) / (n ^ (2) + n + 1)) +

Find the value of ( 1 - 1/3 ) ( 1 - 1/4 ) ( 1 - 1/5 ) ---------- ( 1 - 1/n ) is ( a ) 2/n ( b ) 4/n ( c ) 3/n ( d ) 5/n

For n in N ,if tan^(-1)((1)/(3))+tan^(-1)((1)/(4))+tan^(-1)((1)/(5))+tan^(-1)((1)/(n))=(pi)/(4) ,then (n-2)/(15) is equal to

Prove : C_0 + 1/3C_2 + 1/5 C_4 + 1/7 C_6 + ………… = (2^n)/(n+1)

Prove that .^(n-1)C_(3)+.^(n-1)C_(4) gt .^(n)C_(3) if n gt 7 .

tan^(-1)((n)/(n+1))-tan^(-1)(2n+1)=(3 pi)/(4)

Prove that: tan^(-1)((m)/(n))+tan^(-1)((n-m)/(n+m))=[(pi)/(4)(m)/(n)>;-1(-3 pi)/(4)(m)/(n)<-1