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Algebra

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Joined:	28 Feb 2007
Post:	2173

5 Apr 2008 12:58:38 IST

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$\text{Find} \ \sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}} + \sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+...+ \sqrt{1+\frac{1}{2007^2}+\frac{1}{2008^2}}$

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sandeep ramesh

Blazing goIITian

Joined: 13 Mar 2008

Posts: 1183

5 Apr 2008 13:00:40 IST

Like 2 people liked this

this was my iit sir test question.

tr = n^2+n+1/n^2+n

answer is 2008-1/2008

Brad

Moderator

Joined: 9 Sep 2007

Posts: 647

5 Apr 2008 13:28:56 IST

Like 4 people liked this

rth term ,

[1 + 1/r² + 1/(r+1)²]

=

[ r⁴ + r² + 1 + 2r³ + 2r²+ 2r / [r(r+1)]² ]

=

[(r²+ r + 1) 2 / [r(r+1)]² ]

= r² + r + 1 / (r² + r) = 1 + 1/r(r+1) = 1 + 1/r - 1/r+1

Too lazy

Atleast take a little pain to type it for others' benefit.

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