**Question 1:**

Prove that if n is an even integer, then

**Question 2:**

If , , , …. are the coefficients in the expansion of , when n is a positive integer, prove that

(a)

(b)

(c) , or , according as n is odd or even.

**Question 3:**

If denotes the sum of the first n natural numbers, prove that

(a)

(b)

**Question 4:**

If , prove that

(a)

(b) .

**Question 5:**

Find the sum of the products, two at a time, of the coefficients in the expansion of , where n is a positive integer.

**Question 6:**

If , where n and p are positive integers, and , a proper fraction, show that .

**Question 7:**

If , , , …,, are the coefficients in the expansion of , where n is a positive integer, show that

.

*That’s all for today, folks!*

*Nalin Pithwa.*

### Like this:

Like Loading...

*Related*