Thread: Finding sums involving Arctan

Given that

Arctan (1/n) - Arctan (1/(n+1)) = Arctan (1/((1+n(n+1))

Find

Sum from i = 1 to n:

Arctan (1/((1+i(i+1))

I have split the question into finding the sum of Arctan (1/n) and Arctan (1/(n+1)), and i'm pretty sure this is the correct approach, but I'm not sure where to go from here

Thanks a lot

Originally Posted by Wandering

Given that
Arctan (1/n) - Arctan (1/(n+1)) = Arctan (1/((1+n(n+1))
Find
Sum from i = 1 to n:
Arctan (1/((1+i(i+1))

Note that the sequence of partial sums is a sequence of collapsing sums.
arctan(1)-arctan(1/(N+1)