Question

 

Tính tổng sau bằng cách hợp lí:

\(A=\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{38\times39\times40}\)

Nhanh và đúng nhất mk tick cho 2 bn nha!!!!!>.<

 

Answer 1

Suy ra 2A=2/1x2x3+2/2x3x4+2/3x4x5+......+2/38x39x40

        2A=3-1/1x2x3+4-2/2x3x4+5-3/3x4x5+........+40-38/38x39x40

       2A=1/1x2-1/2x3+1/2x3-1/3x4+1/4x5-1/5x6+........+1/38x39-1/39x40

      2A=1/2-1/1560

      2A=780/1560-1/1560

      2A=779/1560

     A=779/1560:2

     A=779/1560x1/2

   A=779/3120

Answer 2

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.......+\frac{1}{38.39.40}\)

\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+.........+\frac{2}{38.39.40}\)

\(2A=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+....+\frac{40-38}{38.39.40}\)

\(2A=\frac{3}{1.2.3}-\frac{1}{1.2.3}+\frac{4}{2.3.4}-\frac{2}{2.3.4}+\frac{5}{3.4.5}-\frac{3}{3.4.5}+.......+\frac{40}{38.39.40}-\frac{38}{38.39.40}\)

\(2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+.......+\frac{1}{38.39}-\frac{1}{39.40}\)

\(2A=\frac{1}{1.2}-\frac{1}{39.40}\)

\(2A=\frac{1}{2}-\frac{1}{1560}\)

\(2A=\frac{779}{1560}\)

\(A=\frac{779}{1560}:2\)

\(A=\frac{779}{3120}\)