Stats Help

(a) Let z not equal to 1 be a real number and n be a positive integer. Show that
1+z+z^2+z^3+...+z^(n-1)=summand of z^k with lower limit k=0 and upper limit n-1=(1-z^n)/(1-z)
(c) Suppose you toss a coin where the probability of a coin landing on heads is p until either a head appears or a total of n tails has been seen. Let the random variable T be the number of tosses made. Determine the probability mass function of T and use your result from part (A) to verify that the summand of P(X=X subscript k) with lower limit K equals to 1.