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Let

A = 1/(1*3) + 1/(3*5) + 1/(5*7) + ...

and

B = 1/(2*4) + 1/(4*6) + 1/(6*8) + ...

 

Find A/B.

 

Hint: Consider the sum A + B.  Can you relate this sum to A or B?

 Feb 17, 2023
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A = 1/(1*3) + 1/(3*5) + 1/(5*7) + .........==It converges to 1/2

 

B = 1/(2*4) + 1/(4*6) + 1/(6*8) + ........==It converges to 1 / 4

 

A / B == (1/2) / (1/4) ==2

 Feb 17, 2023

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