\(A=\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{2019.2020}\)

\(=9\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2019.2020}\right)\)

\(=9\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2019}-\frac{1}{2020}\right)\)

\(=9\left(1-\frac{1}{2020}\right)\)

\(=9.\frac{2019}{2020}\)

\(=\frac{18171}{2020}\)

\(A=\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{2019.2020}\)

\(A=9.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2019.2020}\right)\)

\(A=9\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2019}-\frac{1}{2020}\right)\)

\(A=9\left(1-\frac{1}{2020}\right)=\frac{9.2019}{2020}=\frac{18171}{2020}\)

...

\(A=\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+...+\frac{9}{2019.2020}\)

\(A=9\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2019.2020}\right)\)

\(A=9\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2019}-\frac{1}{2020}\right)\)

\(A=9.\left(1-\frac{1}{2020}\right)\)

\(A=9.\left(\frac{2020}{2020}-\frac{1}{2020}\right)\)

\(A=9.\frac{2019}{2020}\)

\(A=\frac{18171}{2020}\)

hok tốt!

Ta có : \(\frac{1}{1.2}\)+  \(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+\(\frac{1}{4.5}\)+\(\frac{1}{5.6}\)+\(\frac{1}{6.7}\)

= 1  - \(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{6}\)+\(\frac{1}{6}\)-\(\frac{1}{7}\)

= 1 - \(\frac{1}{7}\)=  \(\frac{6}{7}\)

=1-1/2+1/2-1/3+1/3-1/4+...+1/6-1/7=1-1/7=6/7

1/1 -1/2 +1/2 -1/3 +1/3 -1/4 +1/4 -1/5 +1/5 -1/6 +1/6 -1/7

1/1- 1/7 =6/7

\(S=9,8+8,7+7,6+...+2,1-1,2-2,3-3,4-...-8,9\)

\(=\left(9,8-8,9\right)+\left(8,7-7,8\right)+...+\left(2,1-1,2\right)\)

\(=0,9+0,9+...+0,9\)

\(=0,9\times8=7,2\)

a=1.2+2.3+3.4+4.+....+200.201

3A = 1.2.(3 - 0) + 2.3.(4 - 1) + .... + 200.201.(202 - 199)

3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + .... + 200.201.202

3A = 200.201 . 202

A = 2706800

\(A=1.2+2.3+3.4+...+200.201\)

\(\frac{1}{A}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{200.201}\)

\(\frac{1}{A}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{200}-\frac{1}{201}\)

\(\frac{1}{A}=\frac{1}{1}-\frac{1}{201}=\frac{200}{201}\)

\(A=1:\frac{200}{201}=\frac{1.201}{200}=\frac{201}{200}\)

( Số cuối + Số đầu ) . số số hạng : 2 =a

=3080 nhớ tít

cách mình đúng;

3S = 1.2.3 + 2.3.3 + 3.4.3 + ... + n(n +1)3
= 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) + ...+ n(n + 1)((n + 2) - (n -1))
= 1.2.3 + 2.3.4 - 2.3 + 3.4.5 - 2.3.4 + ... + n(n + 1)(n + 2) - n(n + 1)(n - 1)
= n(n + 1)(n + 2)
=> S = n(n + 1)(n + 2)/3

S = 1.2 + 2.3 + 3.4 + ... + 99.100

3S = 1.2.3 + 2.3.3 + 3.4.3 + .. +99.100.3

3S = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98)

3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100

3S = 99.100.101

3S = 999 900

  S = 333 300

Vậy S = 333 300

\(A = 1 . 2 + 2 . 3 + 3 . 4 + ... + 100 . 101\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+100\cdot101\cdot\left(102-99\right)\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+100\cdot101\cdot102-99\cdot100\cdot101\)

\(3A=100\cdot101\cdot102\)

\(3A=1030200\)

\(A=1030200\text{ : }3\)

\(A=343400\)

\(A = 1 . 2 + 2 . 3 + 3 . 4 + ... + 100 . 101\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+100\cdot101\cdot\left(102-99\right)\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+100\cdot101\cdot102-99\cdot100\cdot101\)

\(3A=100\cdot101\cdot102\)

\(3A=1030200\)

\(A=1030200\text{ : }3\)

\(A=343400\)

Câu hỏi của Nguyen Yen Nhi - Toán lớp 6 - Học toán với OnlineMath

Em xem bài ở link này!

\(S=1.2+2.3+3.4+...+99.100\)

\(\Leftrightarrow3S=1.2.3+2.3.3+3.4.3+...+99.100.3\)

\(\Leftrightarrow3S=1.2\left(3-0\right)+2.3\left(4-1\right)+3.4\left(5-2\right)+...+99.100\left(101-98\right)\)

\(3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)

\(\Leftrightarrow3S=99.100.101\)

\(\Leftrightarrow S=\frac{99.100.101}{3}\)

\(\Leftrightarrow S=33.100.101\)

\(\Leftrightarrow S=333300\)

3S=1.2.3+2.3.3+3.4.3+...+99.100.3=1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)

3S=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-...-98.99.100+99.100.101=99.100.101

S=99.100.101:3=33.100.101