Math Is Fun Forum

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

A series problem

Can anyone please help me out with this problem:

(1/( √ 1+ √ 2))+(1/( √ 2+ √ 3))+(1/( √ 3+ √ 4))................(1/( √ 99+ √ 100))

Please tell me the answer along with explanation.

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Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: A series problem

hi iamaditya

Like this:

This is called rationalising the denominator.  Do this for every term and most bits cancel.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: A series problem

Yeah then we would be getting

( √2- √1)( √3- √2)( √4- √3)........( √100- √99)

Then, how we will proceed next.

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Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: A series problem

In post 1 the terms are added together.  So don't multiply those new terms; add them.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: A series problem

Yeah, I'm extremely sorry. I don't know in which state of mind I was at that time that I did this big mistake. I was about to delete the message but I didn't get time. And thanks for your answer.

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Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam