So this problem is actually an infinite series question, but i have shaved it down to an integral that i cannot seem to solve. I am new to this so i am going to try to talk you through it
here is the original problem:
the sum from n=1 to n=[tex]\infty[/tex] of sin(1/n)
we have learned multiple ways to solve these equations, for this i have decided to use the integral test which says, if the integral from 1 to [tex]\infty[/tex] converges, then the sum converges.
The Attempt at a Solution
so far i have simplified it down to:
the integral from 1 to [tex]\infty[/tex] sin(1/x)dx however 1/x is also equal to x^-1 and taking this anti-derivative leaves me with x all over the place and to many options for an anti-derivative. i was thinking u substitution, any ideas.