Problem 17. Using the following outline prove the limit comparison test:Let Pan and Pbnbe nonegative series. Assume that limanbn=L>0. Thensum Pan converges if and only ifPbn converges.(a) Since limanbn=L there isan integer N such that n>N implies |anbn-L|N implies an<32Lbn.(b) Now assume that Pbn converges. Show that Pk=N+132Lbk converges.(Note the starting index.)(c) Show that Pk=N+1ak converges, and therefore the entire series Panconverges.(d) Show that the converse follows immediately. (Hint: limbnan=L-1.)