# Maths C Question Im having trouble with

1. May 27, 2014

### Digital Genius

1. The problem statement, all variables and given/known data

Evaluate:

99
∑ 1 over √r+1 + √r
r=1

2. Relevant equations

this might be relevant..

the previous question was this, which i managed to solve but it still has the same fraction in it.

Show that: 1 over √r+1 + √r = √r+1 - √r , for r is greater or equal to 0

3. The attempt at a solution

i got as far as...

T1 =

99
∑ 1 over √r+1 + √r
r=1

=0.4142

T2= 2/√2+1 + √2 .....r=2
=0.6357

OR

T2=
99
∑ 1 over √r+1 + √r............................ar^n-1
r=1

a=
1 over √r+1 + √r
.........................ok nevermind i have no clue haha, i did get a bit more then that but just realised it doesnt make sense... thanks for the help in advance :)

2. May 27, 2014

### Pranav-Arora

Hi Digital Genius! Welcome to PF! :)

$$\sum_{r=1}^{99} \frac{1}{\sqrt{r+1}+\sqrt{r}}$$

Hint: Multiply and divide by $\sqrt{r+1}-\sqrt{r}$.

Last edited: May 27, 2014
3. May 28, 2014

### sankalpmittal

If your question is same as stated by Pranav, then rationalize the denominator and convert it two sum of two terms. Then you see that the mid terms cancel.

If it is as you have shown in your attempt, then why, i consider it very difficult or at least very cumbersome.

4. Jun 2, 2014

### Digital Genius

ok well according to my friends its this, but i dont see where they multiplied and divided...

=√99+1 - √r
=√99+1 -√1
=√100 - √1
=10-1
=9

any ideas??

5. Jun 2, 2014

### Staff: Mentor

Use your knowledge of the previous problem. If
$$\frac{1}{\sqrt{r+1}+\sqrt{r}} = \sqrt{r+1}- \sqrt{r}$$
how can you simplify
$$\sum_{r=1}^{99} \frac{1}{\sqrt{r+1}+\sqrt{r}}$$
?