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

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

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

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

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

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

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

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

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

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

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

=2/2 - 2/3 - 2/4 - .........- 2/38 - 2/39 - 2/40

= 2/2 - 2/40

=1   - 2/40

=38/40

= 19/20

mk ko hiểu cho lắm bn có thể giải thích rõ hơn ko ? 

\(=\frac{2}{2}-\frac{2}{3}-\frac{2}{4}-...-\frac{2}{38}-\frac{2}{39}-\frac{2}{40}\)

\(=\frac{2}{2}-\frac{2}{40}\)

\(=1-\frac{2}{40}\)

\(=\frac{38}{40}=\frac{19}{20}\)

Code : Breacker

Bài giải chi tiết:

Ta có:
S = 1 x 2 + 2 x 3 + 3 x 4 + ...+ 38 x 39 + 39 x 40
S x 3 = 1 x 2x 3 + 2 x 3x 3 + 3 x 4x 3 +… + 38 x 39 x 3 + 39 x 40 x 3
S x 3 = 1 x 2 x 3 + 2 x 3 x (4  - 1) + 3 x 4 x (5-2) + ... + 38 x 39 x (40 - 37) + 39 x40 x(41 - 38)
S x 3 = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + ... + 38 x 39 x 40 - 37x 38 x 39 + 39 x 40 x 41 - 38 x 39 x 40.
S x 3 = 39 x 40 x 41
S = 39 x 40 x 41 : 3= 21320

Bỏ số 40 nhỏ ở cuối đi

rút gọn là được mà ! 

\(\frac{1}{2}\)

\(\frac{7}{14}\)

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)

\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2014.2015.2016}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2015.2016}\right)\) 

\(\dfrac{2}{1\times2\times3}+\dfrac{2}{2\times3\times4}+\dfrac{2}{3\times4\times5}+...+\dfrac{2}{48\times49\times50}\)

\(=\dfrac{1}{1\times2}-\dfrac{1}{2\times3}+\dfrac{1}{2\times3}-\dfrac{1}{3\times4}+\dfrac{1}{3\times4}-\dfrac{1}{4\times5}+...+\dfrac{1}{48\times49}-\dfrac{1}{49\times50}\)

\(=\dfrac{1}{1\times2}-\dfrac{1}{49\times50}\)

\(=\dfrac{1}{2}-\dfrac{1}{2450}\)

\(=\dfrac{612}{1225}\)

\(\text{#}Toru\)

1/2 - 1/49 x50

Ta có : S = \(\frac{5.2^{30}.6^3.3^{15}-2^3.8^9.3^{17}.21}{21.2^{29}.3^{16}.4-2^{29}.\left(3^4\right)^5}=\frac{5.2^{30}.\left(2.3\right)^3.3^{15}-2^3.\left(2^3\right)^9.3^{17}.3.7}{3.7.2^{29}.3^{16}.2^2-2^{29}.3^{20}}=\frac{5.2^{33}.3^{18}-2^{30}.3^{18}.7}{3^{17}.7.2^{31}-2^{29}.3^{20}}\)

\(=\frac{2^{30}.3^{18}.\left(5.2^3-7\right)}{3^{17}.2^{29}.\left(7.2^2-3^3\right)}=2.3.33=198\)

\(=\frac{1.2}{99.100}\)

\(=\frac{2}{9900}=\frac{1}{4950}\)