Hello course team, I need help formulating the following calculus two problems. Please show work and explanation.

Problem # 1 (20 points) State whether series converges or diverges and provide reasons for your conclusions A. 1 L0 (1) ;(_1) () - 2 _13\\yn+1 Problem # 2 (10 points) Determine whether the given series Converge Absolutely, Converge Conditionally, or Diverge and give reasons for your conclusions co i _1 n+1 Z( ) 3+ n? n=3 Problem # 3 (20 points) Apply the Ratio Test and state the conclusion. A n! n=3 Problem # 4 (20 points (a) find all values of x for which each given power series converges (b) graph the interval of convergence for the series on a number line (c ) check the end points Problem # 5(10 points) Use the substitution method and a known power series to find power series for the given functions 1 1 1 ='@ Problem # 6 (10 points) Calculate the first five terms of the Taylor series for the given functions at the given point c sin(x), for c=m Problem # 7 (10 points) Calculate the Taylor polynomials P, P, P,, P5, for the given function centered at the given value of flx) =%, =1