Hi,

I need some help with this big theta proof:

Show that f(n) = summation (from h=1 to n) of h^{3}/2^{h}is big theta(1).

What I got so far:

omega(g(1)) <= f(n) <= O(g(1))

c_{1}g(1) <= f(n) <= c_{2}g(1)

For f(n) <= O(1)

f(n) = summation (from h=1 to n) of h^{3}/2^{h}<= 1c_{2}

f(n) = 1/2 + 8/4 + ... + n^{3}/2^{n}<= c_{2}

1/2 <= c_{2 }and 8/4 <= c_{2 }... and n^{3}/2^{n}<= c_{2 }

Since n^{3}/2^{n}is the biggest term in the summation, then showing n^{3}/2^{n}<= c_{2}is enough to show that f(n) <= O(1).

And here is where I get stuck, I'm not sure what to do next...