Calculation (1 + 1 / 1x3) (1 + 1 / 2x4) (1 + 1 / 3x5) (1 + / 4x6) (1+/11×13)

Calculation (1 + 1 / 1x3) (1 + 1 / 2x4) (1 + 1 / 3x5) (1 + / 4x6) (1+/11×13)

I've worked out the problem, but I forgot

The results of (1 + 1 / 1x3) x (1 + 1 / 2x4) x (1 + 1 / 3x5) X... x (1 + 1 / 9x11) process are all necessary

The original formula = [(3 + 1) / 3] * [(4 + 2) / 4] * [(5 + 3) / 5] *... * [(11 + 9) / 11] = [(2 * 2) / 3] * [(2 * 3) / 4] * [(2 * 4) / 5] *... * [(2 * 10) / 11] = [(2 ^ 9) * (2 * 3 * 4 *... * 10)] / (3 * 4 * 5 *... * 11) = 1024 / (10 * 11) = 512 / 11

1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13=

1/1x3 = （1-1/3)/2
1/3x5 = (1/3-1/5)/2
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.
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1/11x13 = (1/11-1/13)/2
All the above are added up
Original formula = (1-1 / 13) / 2 = 6 / 13

(1x3) 1 + (3x5) 1 + (5x7) 1 + (7x9) 1 + (9x11) 1

1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+(1/9-1/11)/2.
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)/2
=(1-1/11)/2
=(10/11)/2
=5/11