Problem about problem solving I am having some problems on how to solve problems. When I read a chapter on say group theory or real analysis, I feel that I have understood the concepts quite well, but when I start solving exercises, after 5 or 6 problems I get stuck. When I see a tough problem, I get messed and cannot find how to come out of it. When I see the solution I have no problem in understanding it. I think about many things but cannot come up with a solution. Is it a problem of my basics not being right? I have an entrance exam & being in this situation is frustrating for me. Please help.

suppose {T} is a collection of bounded operators on a Hilbert space H, with  IT<1   for all k. Suppose also that.
Let SN - Σ Ν T k =-Ν
Show that SNf)     converges as N00 , for every Є Н . If  Tf denotes the limit, prove that  |T||< 1 . [Hint: Consider first the case when only finitely many of the  TK are non-zero, and note that the ranges of the TK are mutually orthogonal.]
