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Functional Analysis

Convergence Series Problem

Please tell me if the following (see attached) series converge. This is a problem from my text book and unfortunately there are no solutions for this problem. I need justification, not just a yes it converges or no it doesn't answer. Determine whether or not the following converge:

Setting Up Triangle Problems

In the problem we are asked to solve for x and y. I can solve for the triangles but not able to use them to find the answer. can someone guide me.

Theta Diagram Functions

I would like some assistance in setting up this problem to solve. In the diagram Theta is 50 degrees and x is the unknown. Thank You