SOLUTION: what is the sum of the coefficients in the expansion of (a+b)^5

Question 391108: what is the sum of the coefficients in the expansion of (a+b)^5
Found 2 solutions by rfer, richard1234:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
a^5+b^5
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We could expand the expression, but there's a much faster way. If you know the binomial theorem, as well as the 5th row of Pascal's triangle, you can easily expand the expression and obtain

The sum of the coefficients is 1 + 5 + 10 + 10 + 5 + 1 = 32. In fact, the sum of the coefficients of any binomial expression is . Can you prove that it works for all positive integers n? (Hint: it relies on Pascal's triangle. Some induction would work nicely)
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