Macroeconomic questions

a. Prove this statement: "If x is less than one, the sum goes to 1/(1-x) as n gets large. If x is equal to or greater than one, the sum explodes as n gets large." b. Consider the present value of a payment of $1 forever, starting next year, when the interest rate is i. The present value is given by: + .. . (1 + i) (1 + 1)2 which can be simplified to: Show the process of simplification. c. Show that: 1 - Ili+1 + 1 +r ( 1 +r)(l+ )(- )mitz + ... Is equal to