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1. Determine if the given series are convergent or divergent. To obtain full credit, clearly state the name of the convergence test or theorem used, and the necessary details leading to your conchision. (a) :2 \"12\") (c) g (13) 2. Evaluate S = _ an for the given sequences. 7L=() 2+ 37 (a) an (b) an 5n n(n + 1) Hint: C (c . an + d . bn) = cCan + d Ebn3. Let f(x) = In(1 + x), complete all parts. (a) Find the power series for f(x) (leave answer in sigma notation). (b) Find the interval of convergence, I, of the power series of f (x). (c) Find In(1 - x2 )d.x.4. Complete all parts. (a) Write the equation of a plane with normal 71.) = ( 2, 5, 3) and containing point P0 (, U, 5) l (b) Determine whether P1 (5, 2, 9) and P2 [2, 1,5) belong on the plane from (a). (c) Compare the plane from (a) with -J: +4[y 2) + 6(z 5) = U do these two surfaces intersect? If yes, at what angle? ((1) Develop a general formula for the distance between a plane and a point (using projections). Then nd the distance between the plane --$ + 4(y 2) + 6(2: - 5) = (J and the origin