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Algebra

Cool goIITian

 Joined: 23 Dec 2011 Post: 70
21 Feb 2012 13:24:24 IST
4 People liked this
5
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Summation (AGS).
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

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

New kid on the Block

Joined: 21 Feb 2012
Posts: 1
21 Feb 2012 14:10:34 IST
1 people liked this

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

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
21 Feb 2012 14:20:55 IST
3 people liked this

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...

Cool goIITian

Joined: 7 Jul 2011
Posts: 59
22 Feb 2012 15:12:41 IST
0 people liked this

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

Cool goIITian

Joined: 7 Jul 2011
Posts: 59
22 Feb 2012 15:13:56 IST
0 people liked this

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

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
22 Feb 2012 18:08:50 IST
0 people liked this

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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