Question

1/2 + 1/6 + 1/12 + 1/20 + ...... + 1/420 + 1/462

Ai trả lời nhanh nhất mk tk

Answer 1

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+......+\frac{1}{420}+\frac{1}{462}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{20.21}+\frac{1}{21.22}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{20}-\frac{1}{21}+\frac{1}{21}-\frac{1}{22}\)

\(=1-\frac{1}{22}\)

\(=\frac{22}{22}-\frac{1}{22}=\frac{21}{22}\)

Answer 2

  ta có      1/2+1/6+1/12+1/20+....+1/420+1/462

            =1/1*2+1/2*3+1/3*4+.......+1/20*21+1/21*22

      =1/1-1/2+1/2-1/3+1/3-1/4+.....+1/20-1/21+1/21-1/22

      =1-1/22=21/22