Subject: Math: Binomial Thrm.
Name: Angela
Question:
First, I expanded the (x+y)
1/(x But I don't know how to expand the last two. I tried to and got:
(x I don't know if I did those right. I don't understand how this relates to the Bionomial Thrm. and what Newton found. Please help me! I'm desperate!! Thank you so much! Hi Angela For n a positive integer and
the Binomial Theorem states that
Newton generalized this for n not a positive integer. The easiest example comes from looking at the identity
which is valid provided x is not 1. To see that this is valid multiply both sides by 1-x.
(Why can't x = -2 or 3 ?) This agrees with the pattern in the statement of the binomial theorem above if a = 1, b = -x and n = -1
It was this kind of observation that led Newton to postulate the Binomial Theorem for rational exponents.
For your first example write (x+y)
with b = y/x and then multiply each term by x
Simularly for fractional exponents. For example in your second problem write (x+y) You need to know some calculus to study the Binomial Theorem for rational exponents and to determine for what values of x it is true.
I hope this helps, |

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