Question

solve this please....

Answer 1

tan ^ -1 ( 1/ ( 1 + n( n+1))

tan^ -1 ( n+1 - n)/ 1 + n ( n+1))

As tan^ -1( x -y)/ 1 + xy = tan^ -1 x - tan^-1 y

So tan^ -1 ( n +1) - tan^ -1 (n)

So

tan^ -1 (2) - tan^ -1 (1)+ tan^ -1( 3) - tan^ -1( 2)

+ tan^ -1( 4) - tan^-1( 3).........tan^ -1( n+1) - tan^ -1(n)

So it will give - tan^ -1 (1)+ tan^ -1( n+1) = tan^-1@

tan^ -1( n +1 -1)/ 1 + n+1)= tan^-1@

tan^ -1 ( n)/ 2 +n = tan^ -1 @

compare

n/ ( 2 + n)= @