# Mathematical induction

1. May 7, 2010

### elitewarr

1. The problem statement, all variables and given/known data
All the terms of the arithmetic progression u1,u2,u3...,un are positive. Use mathematical induction to prove that, for n>= 2, n is an element of all positive integers,

[ 1/ (u1u2) ] + [ 1/ (u2u3) ] + [ 1/ (u3u4) ] + ... + [ 1/ (un-1un) ] = ( n - 1 ) / ( u1un)

2. Relevant equations

3. The attempt at a solution
I proved that P(2) is true. However, I tried to prove that P(K+1) is true but to no avail.

Thanks.

2. May 7, 2010

### vela

Staff Emeritus
Use the fact that {un} is an arithmetic sequence along with

$$\frac{1}{u_m} - \frac{1}{u_n} = \frac{u_n-u_m}{u_mu_n}$$

3. May 9, 2010

### elitewarr

Solved. Thanks a lot!

4. May 10, 2010

### ripcity4545

This helped a lot for me on the induction concept:

http ://en. wikipedia. org/wiki/Mathematical_induction

5. Jun 26, 2011

### claire44

i know this thread is old... but i need a little help on the exact same question...

i'm stuck at:

$$P(k+1)=\frac{kU_{k+1}-U_{k+1}+U_1}{U_1U_kU_{k+1}}$$

i need to prove that this equals to:

$$\frac{k}{U_1U_{k+1}}$$

but i can't see the link at all... is there something missing ?~

6. Jun 27, 2011

### Staff: Mentor

What do you have for your induction hypothesis? I.e., P(k).