Question

How to find sum of coefficients in binomial expansion?

Answer 1

Step-by-step explanation:

Teh sum of coefficients is

$- b \div a$

Thank you

Answer 2

Answer:

Step-by-step explanation:

The sum of the coefficients of the terms in the expansion of a binomial raised to a power cannot be determined beforehand, taking a simple example -

(x+1)2=x2+2x+1,∑Cx=4

(x+2)2=x2+4x+4,∑Cx=9

This is because of the second term of the binomial - which is a constant. This constant will also contribute to the coefficients of the terms.

What is a binomial coefficient?

According to the binomial theorem, the (r+1)th term in the expansion of (x+a)n is,

Tr+1=nCrxn−rar

You can see the nCr being used here - which is the binomial coefficient. The sum of the binomial coefficients will be 2n because, as we know that -

∑nr=0(nCr)=2n

What is the difference between a binomial coefficient and the actual coefficient of the terms?

In the expansion of (x+a)n, if a is a constant, then the actual coefficient of the (r+1)th term will be the product of ar and the binomial coefficient for that term.

NOTE: The sum of the coefficients of (x+1)n will be  2n  because all the powers of 1 will result in one - making the binomial coefficients and actual coefficients equal.