Problem 1

n=0 to infinity (-1/2)^n (x-3)^n

How would you find the value of x for which the given geometric series converges and how would you find the sum of the series(as a function of x) for the value of x?

Problem 2

How would you find the values of b for which

1+ e^b+ e^2b+ e^3b+.....=9