Can someone solve this problem.....I really need the solution....I have always been bad at statistics

To create polymer molecules-linear strings of monomer units linked togehter like beads on a necklace-chemists start wit monomers in solution and intiate polymerization conditions. Monomers add to the ends of growing chains one unit at a time. Because the process is random some chaings are long, some are short. There is a distribution of molecular weights.

Suppose p is the probablility that a monomer unit is reacted and connected in the chain.

a) show that distribution of chains with length k is

p_{k}=n_{k}\sum_{k=1}^{\infty} n_{k} with

b) calculate the average chain length

in experiments one measures the molecular weight distribution

c) show that

d) compute the average molecular weight