Hi all

I want check my anwsers

3 – If r = -1 and frist term is 1/2 find the sum of the 10 terms of a Gp

4 - Use mathematical induction to prove that 2 + 4 + 6 ……..+ 2n = n(n+1)

5 – Expand ( 2x – 3y)^4 by using binomial formula

Results 1 to 4 of 4

- Feb 14th 2010, 06:13 AM #1

- Joined
- Oct 2009
- Posts
- 290

- Feb 14th 2010, 06:24 AM #2

- Feb 14th 2010, 06:58 AM #3

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,028
- Thanks
- 847

Hello, r-soy!

3) If and first term is ,

find the sum of the first 10 terms of the GP.

We have: .

Therefore: .

4) Use mathematical induction to prove that: .

Assume

Add to both sides: .

And we have: .

We have proved . . . The proof is complete.

5) Expand: .

. . .

. . . .

. . .

- Feb 14th 2010, 07:12 AM #4

- Joined
- Apr 2005
- Posts
- 18,862
- Thanks
- 2707

For (1) you have used r= 10 in the denominator when r= -1.

(And, by the way, if it were 10, 1- 10= -9, not -11!)

For (2) you are fine until you get to and there you stop. Don't forget what you are trying to prove. You want to prove that sum is n(n+1) which, for n= k+1, is (k+1)(k+2). Factor !

For (3), has mysteriously become !