A note on doing symbolic computations

If some of you are unsure of your summing or calculus knowledge, you can check your answers by using the symbolic computation facility in matlab, here are some simple examples:

k=sym('k');
%This tells the system to treat k as a symbol not a vector.

symsum(k^2)                   1/3*k^3-1/2*k^2+1/6*k

symsum(1/k^2,1,Inf)           1/6*pi^2

You can also do Taylor expansions:

x=sym('x') 
taylor(exp(-x))
1-x+1/2*x^2-1/6*x^3+1/24*x^4-1/120*x^5