# Expanding Summation with terms

I'm trying to expand this series:

Sum[(Binomial[n - 1, k]*(-1)^k*(θ/T)^(n - 1 - k))/
(m - (k + 1)*α), {k, 0, n - 1}]


to look something like this:

1/(m - 5 α) - (4 (θ/T)^α)/(m - 4 α) + (6 (θ/T)^(2 α))/(m - 3 α) -
(4 (θ/T)^(3 α))/(m - 2 α) + (θ/T)^(4 α)/(m - α)


But I keep getting things like this..

(-2 m^3 α (5 T - 7 θ) (T - θ)^3 + m^4 (T - θ)^4 +
m^2 α^2 (T - θ)^2 (35 T^2 - 94 T θ + 71 θ^2) +
24 α^4 (T^4 - 5 T^3 θ + 10 T^2 θ^2 - 10 T θ^3 + 5 θ^4) -
2 m α^3 (25 T^4 - 122 T^3 θ + 234 T^2 θ^2 -
214 T θ^3 + 77 θ^4))/(T^4 (m - 5 α) (m - 4 α)
(m - 3 α) (m - 2 α) (m - α))


So, how expand summation to look more like

1/(m - 5 α) - (4 (θ/T)^α)/(m - 4 α) + (6 (θ/T)^(2 α))/(m - 3 α) -
(4 (θ/T)^(3 α))/(m - 2 α) + (θ/T)^(4 α)/(m - α)


Also, how can I format code in here better when I ask questions?

• Feb 18 '17 at 16:54
• Thanks, but how can I get the symbols like "Sigma" - I.e., have it look just like in my notebook...
– PiE
Feb 18 '17 at 17:07
• The object should be to make it easy for others to copy and paste your code so that they can provide help--not to make it look like your notebook. Feb 18 '17 at 17:12

I am not sure what you're trying as you didn't include that, but on my system:

n = 5;

Sum[(Binomial[n - 1, k]*(-1)^k*(θ/T)^(n - 1 - k))/(m - (k + 1)*α), {k, 0, n - 1}]


• Wow. Really? I just ran the same command on my system and put it in a closed form expression - the Hypergeometric Function 2F1...Wierd...What do you think is going on?
– PiE
Feb 18 '17 at 18:01
• Never mind the previous comment...Sorry...I'm kind of new to Mathematica stuff...When I type i "n = 5", and input it, then this works...
– PiE
Feb 18 '17 at 18:04