SOLUTION: Find the sum of the series {{{ 5/(sqrt (2) + sqrt (1)) + 5/(sqrt (3) + sqrt (2)) + 5/(sqrt (4) + sqrt (3)) +5/(sqrt (5) + sqrt (4)) +... }}} + {{{ 5/(sqrt (36) + sqrt (35)) }}}

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Question 1104112: Find the sum of the series +
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!

Let's look at the sum of the first few terms of the series; then you can use that to predict the sum of the whole series.

So the sum of the first three terms of the series is

You can see that the terms with sqrt(2) and sqrt(3) cancelled, leaving only sqrt(4) and sqrt(1).

The last term in the series is going to be equivalent to

Can you see what you are going to be left with when you add all the terms of the series and cancel where possible?

Answer by ikleyn(52769)   (Show Source):
You can put this solution on YOUR website!
.
For this and other similar series see the lesson
    - Amazing calculations with fractions that contain quadratic irrationalities in denominators
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Evaluation, substitution".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.