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Maths C Question Im having trouble with

  1. May 27, 2014 #1
    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. jcsd
  3. May 27, 2014 #2
    Hi Digital Genius! Welcome to PF! :)

    I assume your question is:
    $$\sum_{r=1}^{99} \frac{1}{\sqrt{r+1}+\sqrt{r}}$$

    Hint: Multiply and divide by ##\sqrt{r+1}-\sqrt{r}##.
     
    Last edited: May 27, 2014
  4. May 28, 2014 #3
    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.
     
  5. Jun 2, 2014 #4
    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??
     
  6. Jun 2, 2014 #5

    DrClaude

    User Avatar

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