Question

Solve this limit question

Answer 1

tr = r/(1+ r^2 + r^4)

= r/( r^2 +1)^2 - r^2

= r/( r^2 + 1+ r)( r^2 + 1 - r)

= r^2 + 1+ r)- ( r^2 + 1 - r))/2( r^2+1-r)(r^2+1+r)

=1/2. ( 1/r^2+1- r. - 1/r^2+ 1+ r)

Summation from r= 1 to n

1/2( 1 - 1/3 + 1/3 - 1/7 +1/7.......1/n^2+1+n)

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1/2 ( 1- 1/n^2+ 1+ n)

1/2( n^2 + 1+ n - 1)/n^2 +1+ n

1/2( n^2 + n)/( n^2 + n +1)

1/2( 1+ 1/n)/( 1 + 1/n + 1/n^2)

put n = infinity

1/2( 1+0)/( 1+0 +0)

1/2

✌✌Dr.Dhruv✌✌

Answer 2

Answer:

tr = r/( 1+r^2+r^4)

= r/( r^2+1)^2-r^2

= r/(r^2+1+r) (r^2+1-r)

= (r^2+1+r)-(r^2+1-r) /2(r^2+1-r)(r^2+1+r)

= 1/2 (1/r^2+1-r-1/r^2+1+r)

Step-by-step explanation:

Hope it helps you ✌✌