7 / 6 + 13 / 12 + 21 / 20 + 31 / 30 + 421 / 420

7 / 6 + 13 / 12 + 21 / 20 + 31 / 30 + 421 / 420

Upstairs, you have learned how to do wrong? The original formula = 1 + 1 / 6 + 1 + 1 / 12 + 1 + 1 / 20 + +1+1/420=19+1/(2*3)+1/(3*4)+1/(4*5)+…… +1 / (20 * 21) notice that 1 / (n * (n + 1)) = 1 / n-1 / (n + 1), so the original formula = 19 + 1 / 2-1 / 3 + 1 / 3-1 / 4 + 1 / 4-1 / 5 + +1/20-1/21=19+1/2-1/21=817/...

Calculate 3 / 2 + 7 / 6 + + 13 / 12 + 21 / 20 four hundred and twenty-one-420ths

3 / 2 + 7 / 6 + 13 / 12 + 21 / 20 four hundred and twenty-one-420ths
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+.+(1/20-1/21)+1×20
=1-1/21 + 20
=20 and 20 / 21

7/6+13/12+21/20+31/30+.421/420

7/6+13/12+21/20+31/30+.421/420
=1+1/6+1+1/12+1+1/20+...+1+1/420
=19×1+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/20-1/21)
=19+1/2-1/3+1/3-1/4+1/4-1/5+...+1/20-1/21
=19+1/2-1/21
=19+21/42-2/42
=19 and 19 / 42;
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