c, 4C= (1.2.3+2.3.4+3.4.5+...+8.9.10) .4

==> 4C= [1.2.3.(4-0) + 2.3.4-(5-1) + 8.9.10.(11-7)

==>4C= 1.2.3.4 - 1.2.3.4+ 2.3.4.5-2.3.4.5 + 7.8.9.10- 7.8.9.10 + 8.9.10.11

==> 4C= 8.9.10.11=7920

==> C= 7920 :4=1980

a, Ta có: 3A= 1.2.3+2.3.3+3.4.3+...+99.100.3

               3A=1.2.(3-0) + 2.3.(4-1)+ 3.4.(5-2)+ ... + 99.100.( 101-98)

               3A=(1.2.3 + 2.3.4+ 3.4.5+ 99.100.101) - (0.1.2 +1.2.3+ 2.3.4 + ... + 98.99.100)

               3A= 99.100.101 - 0.1.2

               3A= 999900 - 0

               3A= 999900

    ==> A= 999900 : 3

   ==> A= 333300

\(B=\dfrac{1}{1.2.3}+\dfrac{1}{3.4.5}+...+\dfrac{1}{8.9.10}\)

\(B=2.\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\)

\(B=2.\left(1-\dfrac{1}{10}\right)\)

\(B=2.\dfrac{9}{10}\)

\(B=\dfrac{9}{5}\)

anh ơi , đại học rồi mà ko giải đc bài này ạ?

hmm

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\)

\(A=\frac{1}{2}\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{10-8}{8.9.10}\right)\)

\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)

\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{9.10}\right)=\frac{11}{45}\).

Phương trình tương đương với: 

\(\frac{11}{45}x=\frac{22}{45}\Leftrightarrow x=2\).

\(A=1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+99\cdot100\cdot\left(101-98\right)\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+99\cdot100\cdot101-98\cdot99\cdot100\)

\(3A=99\cdot100\cdot101\Rightarrow A=\dfrac{99\cdot100\cdot101}{3}=333300\)

\(B=1^2+2^2+3^2+...+99^2+100^2\)

\(=\dfrac{100\cdot\left(100+1\right)\cdot\left(2\cdot100+1\right)}{6}\)

\(=\dfrac{2030100}{6}=338350\)

\(C=1\cdot2\cdot3+2\cdot3\cdot4+...+8\cdot9\cdot10\)

\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+...+8\cdot9\cdot10\cdot\left(11-7\right)\)

\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+8\cdot9\cdot10\cdot11-7\cdot8\cdot9\cdot10\)

\(4C=8\cdot9\cdot10\cdot11\Rightarrow C=\dfrac{8\cdot9\cdot10\cdot11}{4}=1980\)

@Hồng Phúc Nguyễn

A = 1 . 2 + 2 . 3 + 3 . 4 + 99 . 100

3A = 1 . 2 . 3 + 2 . 3 . (4 - 1) + 3 . 4 . (5 - 2) + ... + 99 . 100 . (101 - 98)

3A = 1 . 2 . 3 + 2 . 3 . 4 - 2 . 3 . 1 + 3 . 4 . 5 - 3 . 4 . 2 + ... + 99 . 100 . 101 - 99 . 100 . 98

3A = 99 . 100 . 98

A = 33 . 100 . 98

A = 323400

gọi A=................................

=>2A=2/1.2.3+2/2.3.4+.....+2/8.9.10

2A=1/1.2-1/2.3+1/2.3-...+1/8.9-1/9.10

2A=1/1.2-1/9.10=22/45 =>A=11/45

Câu hỏi của Kudo Shinichi - Toán lớp 6 - Học toán với OnlineMath

Tham khảo tại link trên chỉ cần nhấn vào .

Chúc bạn học tốt

              \(2Z=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\) 

              \(2Z=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\)

              \(2Z=\frac{1}{1.2}-\frac{1}{9.10}\)

              \(2Z=\frac{22}{45}\)

               \(\Rightarrow\frac{22}{45}.x=\frac{22}{45}\)

                              \(x=\frac{22}{45}:\frac{22}{45}\)

                              \(x=1\)