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Algebra

Cool goIITian

Joined:	23 Dec 2011
Post:	70

21 Feb 2012 13:24:24 IST

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330

Summation (AGS).

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

Sum to infinity: 1 + 1/5 +3/5sq + 5/5cb.......

Comments (5)

yeshwendra shukla

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Joined: 21 Feb 2012

Posts: 1

21 Feb 2012 14:10:34 IST

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find nth termand then apply method of difference..u'll get the result

hemang

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Joined: 27 Dec 2010

Posts: 1508

21 Feb 2012 14:20:55 IST

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let x = 1 + 1/5 + 3/5^2 + 5/5^3 ....

x/5 = 1/5 + 1/5^2 + 3/5^3 ....

on subtracting we get,

4x/5 = 1 + 2/5^2 + 2/5^3 + ...

4x/5 = 1 + 2(1/5^2 + 1/5^3 + ...

4x/5 = 1 + 2(1/25)/(1-1/5)

4x/5 = 1 + 1/5 = 6/5.

x = 3/2.

there may be some mistake. i am dizzy...

Abhishek Bandiya

Cool goIITian

Joined: 7 Jul 2011

Posts: 59

22 Feb 2012 15:12:41 IST

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a little bit mistake ,but concept of you two is exactly right,only this matters

Abhishek Bandiya

Cool goIITian

Joined: 7 Jul 2011

Posts: 59

22 Feb 2012 15:13:56 IST

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a little bit mistake ,but concept of you two is exactly right,only this matters

hemang

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Joined: 27 Dec 2010

Posts: 1508

22 Feb 2012 18:08:50 IST

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i found my mistake now.

sorry for it.

4x/5 = 1 + 2(1/25)/(1-1/5)

then 4x/5 = 1 + 1/10 = 11/10.

so, x = 11/8 = 1.375

done.... thanks abhishek. appreciate it.

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