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

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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) About Me  (Show Source):
Answer by richard1234(7193) About Me  (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

a%5E5+%2B+5a%5E4b+%2B+10a%5E3b%5E2+%2B+10a%5E2b%5E3+%2B+5ab%5E4+%2B+b%5E5

The sum of the coefficients is 1 + 5 + 10 + 10 + 5 + 1 = 32. In fact, the sum of the coefficients of any binomial expression %28a%2Bb%29%5En is 2%5En. Can you prove that it works for all positive integers n? (Hint: it relies on Pascal's triangle. Some induction would work nicely)