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?
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
