Chi-squaredk distribution proof

The information I have been given is:

If X1,...,Xk are independent N(0,1) random variables, then

W = (X1)^2 + (X2)^2 + ... + (Xk)^2

has a Chi-squaredk distribution, where k is the degrees of freedom (number of independent squares in the sum of W)

Show that:

If Z1 ~ Gamma (alpha1, beta) and Z2 ~ Gamma (alpha2, beta); Z1 and Z2 are independent, then Z = Z1 + Z2 ~ Gamma(alpha1+alpha2, beta).

Hence show that W ~ Gamma (k/1, 1/2)

(on a sidenote, can you tell me or point me in the direction on how to type in the mathematical format? like a website or page to tell me to type in mathematical formulas, instead of the way i do it now, which is just in word format)

Thanks!

Ynotidas