# Binomial Theorem problem

1. Jul 31, 2013

### Miike012

I highlighted the portion in red in the paint document that I'm not understanding.

How can we see by inspection that the product is equal to the series 2?

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2. Jul 31, 2013

### pasmith

The term independent of x in the product is equal to the series (2); this is because the term independent of x is a sum of terms of the form $kc_k x^k \times c_k/x^k = kc_k^2$.

3. Jul 31, 2013

### Miike012

The second line in the paint document is equal to n/xn(1 + (2n-1)x + (2n-1)(2n-1)/2!x2 + .....) by using the binomial theorem

If we look at the coefficient of the second term it is equal to n(2n-1).

If we compare the coeff. n(2n -1) with the coeff. of the second term of series (2) which is
2c22 = 2(n-1)(n-2)/2! = n2 - 3n + 2 they are not equal.

Hence n(2n-1) =/= n2 - 3n + 2

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4. Jul 31, 2013

### Miike012

Never mind I see that u said its the sum of the terms.... I got it now