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Find the value of 1/(2 2 +-1)+1/(4 2 -1)+1/(6 2 -1)...... ...+1/(20 2 -1)

Find the value of 1/(22+-1)+1/(42-1)+1/(62-1)......
...+1/(202-1)

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
1/(2^2+-1)+1/(4^2-1)+1/(6^2-1)......
...+1/(20^2-1)
= a^2 -b^ = (a+b)(a-b) 
Put this formula and multiply and divide by 2 
= {2/(2+1)(2-1) + 2/(4+1)(4-1) +..... 2/(20-1)(20+1) ) }*1/2
we can write numerator where there is 2 as (2+1)- (2-1) similarly 
we can also write 2 as (4+1)-(4-1) 
The equation will become 
[1/(2-1)  - 1/(2+1) +1/(4-1) -1/(4+1) ...1/(20-1) -1/(20+1) ] *1/2 
On simplifying 
[1-1/3 + 1/3 -1/5 +1/5 ...........-1/19 -1/21 ] *1/2 
Cancel all the term 
and simplify 
ans = 10/21 

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