3 of the questions remain unanswered. (15 points) Consider the following infinite series. 00 r = 1 +r+r + +... x=0) Note: In the series above, x is the index of the summation. If r is between -1 and 1 (e.g. [r] < 1 ), the infinite series has a closed form expression. 00 px = 1+r+r + p +. = x=0 Express the following series as a function of r. 1 1-r if |r| < 1 C. 8 xr-x 1/(1-r) x=0 d. x(x - 1)p-x-2 x=2 e. Hint for part(d): = 00 00 x(x - 1)r-* = x=2 f. xr= x=0 Hint for part(f): x = x(x-1) + x d dr2 00 = e. For any t, epx = x=0 2/(1-r)^3 ift < = x(x - 1)px-2 1/(1-r)^3 Hint for part(e): For any constant a and b, abb = (ab)". (Enter a function of t and r) (Enter a function of r)