Question

How many terms are in the expansion (a + b)^15.

Answer 1

The binomial theorem is the best way to answer this problem. But here's a quick, intuitive way to see how many terms are in (a + b)^15...

(a + b)^1 has 2 terms: a + b
(a + b)^2 has 3 terms: a^2 + 2ab + b^2
(a + b)^3 has 4 terms: a^3 + 3a^2b + 3ab^2 + b^3
...
(a + b)^7 has 8 terms

See the pattern?

Answer 2

so whatever the exponent is, 1 more then that is how many terms there are?

Answer 3

Yes.

This isn't a rigorous proof at all. But it does hold true for the form (a + b)^c when c is positive.

Answer 4

ok cool, thanks a lot