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#1 2013-11-21 17:02:11

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 832

any shortcut?

pls tell me is there any easier way to solve the following:-


friendship is tan 90°.

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#2 2013-11-21 17:25:04

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: any shortcut?

Hi,

Think "partial fractions" and "telescoping series".


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#3 2013-11-21 18:03:39

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 832

Re: any shortcut?

pls explain.


friendship is tan 90°.

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#4 2013-11-21 18:14:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: any shortcut?

Here is a little hint:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2013-11-21 20:49:41

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: any shortcut?

hi niharika_kumar

You'll find every fraction can be split like this and then you can do a lot of cancelling out.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2013-11-23 16:08:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: any shortcut?

Did you get the answer?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2013-11-23 16:10:12

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 832

Re: any shortcut?

and if there is a long series, then is it necessary to compute each one?
don't you think it will be time consuming.


friendship is tan 90°.

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#8 2013-11-23 16:10:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: any shortcut?

Nope, it is rather easy! No computation necessary.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2013-11-23 16:21:40

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 832

Re: any shortcut?

pls. explain


friendship is tan 90°.

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#10 2013-11-23 16:40:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: any shortcut?

Hi;

Now subtract the bottom one from the top one. The technique is called telescoping. Notice the massive cancellations making the sum to any amount of terms easy.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11 2013-11-23 17:40:25

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 832

Re: any shortcut?

so here the answer is

.right?
its a nice method smile but if we have just one equation like

what do we need to do now?


friendship is tan 90°.

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#12 2013-11-23 20:01:38

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 602
Website

Re: any shortcut?

Often in mathematics you just have to be imaginative in going about solving problems.


143 books currently added on Goodreads

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#13 2013-11-23 22:52:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: any shortcut?

Hi;

When you have a series you must guess at the general term. You can play spot the pattern or you can use curve fitting but you will come up with

just as Nehushtan did above. You break it into partial fractions as above:

Now you telescope it out

Now just subtract the bottom from the top, again with massive cancellations.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#14 2013-11-24 22:41:53

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 832

Re: any shortcut?

thanks again! smile
I initially couldn't understand it clearly.
thanks again.....


friendship is tan 90°.

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#15 2013-11-24 23:04:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: any shortcut?

Very good!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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