# Writing summation as $A^B$, where have to find $A$ and $B$.

Write $\sum\limits_{k=0}^{1000} \binom{1000}{k}5^k$ as $A^B$, where have to find $A$ and $B$.

I would love to tell you what I've tried, but I don't even understand the question, so have no idea where to begin. I know I could write $\sum\limits_{k=0}^{1000} \binom{1000}{k}$ as $2^{1000}$, but I don't see how that helps. Feeling pretty stupid :(

• Just take $A = \sum_{k=0}^{1000} \binom{1000}{k}5^k$ and $B = 1$. Commented Oct 5, 2017 at 9:00
• All silliness aside, are you familiar with the binomial theorem? Commented Oct 5, 2017 at 9:01
• @MeesdeVries Yes, that is what we've been studying Commented Oct 5, 2017 at 9:02
• Does the expression you've been given look like one side of the equation in the binomial theorem? That would be a good place to start. Commented Oct 5, 2017 at 9:03
• @MeesdeVries I don't understand this $A$ and $B$ thing tho? How can I express that as some sort of variable we have to find? Commented Oct 5, 2017 at 9:09

Look at $(1+5)^{1000}$. Binomial theorem !