18. laughing

19. to do

20. doing

1. laughing

2. to do

khó à nha

Đặt A = 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 + ... + 17 . 18 . 19 + 18 . 19  . 20

=> 4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . 4 + 3 . 4 . 5 . 4 + ... + 17 . 18 . 19 . 4 + 18 . 19 . 20 . 4

     4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . ( 5 - 1 ) + 3 . 4 . 5 . ( 6 - 2 ) + ... + 17 . 18 . 19 . ( 20 - 16 ) + 18 . 19 . 20 . ( 21 - 17 )

     4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . 5 - 1 . 2 . 3 . 4 + 3 . 4 . 5 . 6 - 2 . 3 . 4 . 5+ ... + 17.18.19.20 - 16.17.18.19 + 18.19.20.21 -17.18.19.20

     4A = 18 . 19 . 20 . 21

 => A = 18 . 19 . 20 . 21 : 4

      A = 35 910

Đặt M = 1.2.3+2.3.4 + 3.4.5+...+17.18.19+18.19.20

=> 4M = 1.2.3.4+2.3.4.4+3.4.5.4+...+17.18.19.4+18.19.20

4M = 1.2.3.(4-0)+2.3.4.(5-1)+3.4.5.(6-2)+...+17.18.19.(20-16)+18.19.20.(21-17)

4M = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ...+17.18.19.20 - 16.17.18.19 + 18.19.20.21 - 17.18.19.20

4M = ( 1.2.3.4 + 2.3.4.5 + 3.4.5.6 + ...+ 17.18.19.20+18.19.20.21) - (1.2.3.4+2.3.4.5+...+16.17.18.19+17.18.19.20)

4M = 18.19.20.21

\(M=\frac{18.19.20.21}{4}\)

=(1/1-1/2-1/3)+(1/2-1/3-1/4)+...+(1/18-1/19-1/20)

=1/1-1/20=19/20

k nha

dung luon nhung van tat qua

Lời giải:

Gọi tổng trên là $A$

$A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{18.19.20}$

$2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{18.19.20}$

$=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+....+\frac{20-18}{18.19.20}$

$=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{18.19}-\frac{1}{19.20}$

$=\frac{1}{1.2}-\frac{1}{19.20}=\frac{189}{380}$

$\Rightarrow A=\frac{189}{760}$

ĐÚNG ĐÓ BẠN ƠI

A = 1/1.2.3 + 1/2.3.4 + ... + 1/18.19.20 

\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{18.19}-\frac{1}{19.20}\right)\)

\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{19.20}\right)\)

\(A=\frac{1}{4}-\frac{1}{2.19.20}< \frac{1}{4}\)

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