Ta có: A=1.2.3+2.3.4+…+98.99.100

=>A.4=1.2.3.4+2.3.4.4+…+98.99.100.4

=>A.4=1.2.3.(4-0)+2.3.4.(5-1)+…+98.99.100.(101-97)

=>A.4=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+…+98.99.100.101-97.98.99.100

=>A.4=98.99.100.101

=>A.4=97990200

=>A=97990200:4

=>A=24497550

Michiel Girl Mít ướt bài lớp 7 đó, lm đi

CT:  

1.2.3...a+2.3.4...(a+1)+......+(n+1)(n+2)....(n+a)

=\(\frac{\left(n+1\right)\left(n+2\right).....\left(n+a+1\right)}{a+1}\)

A = 1.2.3  + 2.3.4  + …. +  98.99.100

4A = 4( 1.2.3  + 2.3.4  + …. +  98.99.100)

4A= 1.2.3.4 + 2.3.4.4 +....+98.99.100.4

4A= 1.2.3.4 + 2.3.4 (5-1) +....+98.99.100(101- 97)

4A= 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + ....+ 98.99.100.101 - 97.98.99.100

4A= 98.99.100.101

4A=97990200

A= 97990200:4

A=24497550

Vậy.....

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}\left(\frac{1}{98.99}-\frac{1}{99.100}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{99.100}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{9900}\right)\)

\(=\frac{1}{2}.\frac{4949}{9900}\)

\(=\frac{4949}{19800}\)

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}\left(\frac{1}{98.99}-\frac{1}{99.100}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{99.100}\right)\)

\(=\frac{1}{2}.\frac{4949}{9900}=\frac{4949}{19800}\)

Đặt S=1.2.3+2.3.4+...+98.99.100

=>4S=1.2.3.4+2.3.4.4+...+98.99.100.4

=>3S=1.2.3(4-0)+2.3.4(5-1)+....+98.99.100(101-97)

=>4S=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+....+98.99.100.101-97.98.99.100

=>4S=98.99.100.101

=>S=24497550

Ta xét:

\(\frac{1}{1.2}-\frac{1}{2.3}=\frac{2}{1.2.3};\frac{1}{2.3}-\frac{1}{3.4}=\frac{2}{2.3.4};...;\frac{1}{98.99}-\frac{1}{99.100}=\frac{2}{98.99.100}\)

Qua công thức trên, bạn có thể rút ra tổng quát: (đây là mình nói thêm)

\(\frac{1}{n.\left(n+1\right)}-\frac{1}{\left(n+1\right).\left(n-2\right)}=\frac{2}{n.\left(n+1\right).\left(n+2\right)}\)

Ta suy ra:

\(2B=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{98.99.100}\)

       \(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\)

      Thấy \(-\frac{1}{2.3}+\frac{1}{2.3}=0;-\frac{1}{3.4}+\frac{1}{3.4}=0;...\)

\(\Rightarrow2B=\frac{1}{2}-\frac{1}{99.100}=\frac{1}{2}-\frac{1}{9900}=\frac{4950}{9900}-\frac{1}{9900}=\frac{4949}{9900}\)

\(\Rightarrow B=\frac{4949}{9900}:2=\frac{4949}{19800}\)

Mình nhầm, công thức tổng quát mình nói thêm bạn đổi cái n-2 thành n+2 nha

 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ............. + 1/ 98.99.100

Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100

4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4

4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100

4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101

4A=98.99.100.101

=>A=98.99.100.101/4

Nói trước , ai làm đúng mình cho 3 tích 

Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100

4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4

4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100

4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101

4A=98.99.100.101

=>A=98.99.100.101/4

Câu hỏi của hồ thị hằng - Toán lớp 6 - Học toán với OnlineMath

\(4D=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+.....+98.99.100\left(101-97\right)\)

\(\Rightarrow4D=1.2.3.4+2.3.4.5-1.2.3.4+.....+98.99.100.101-97.98.99.100\)

\(\Rightarrow4D=98.99.100.101\)

\(\Rightarrow D=\frac{98.99.100.101}{4}\)

\(\Rightarrow D=24497550\)

A= 1.2.3 + 2.3.4 + 3.4.5 +.....+ 98.99.100

4A = 98.99.100.4 + .....+ 3.4.5.4 + 2.3.4.4 + 1.2.3.4

4A = 98.99.100.(101-97) +... + 2.3.4.(5-1) + 1.2.3.4

4A = 98.99.100.101 - 97.98.99.100+......+2.3.4.5 - 1.2.3.4 + 1.2.3.4

4A = 98.99.100.101

  A = 98.99.100.101 : 4

  A = 24497550

24497550

100% đó tick nha

24497550

sssssssss........... đang ngủ

bai toan nay kho qua

mày là thằng nào mạo danh là olm hả?

nhân cả 2 vế với 4; ta có 

4S=1.2.3.4+2.3.4.4+3.4.5.4+....+98.99.100.4

4S=1.2.3.(4-0)+2.3.4.(5-1)+....+98.99.100.(101-97)

4S=1.2.3.4-1.2.3.0+2.3.4.5-1.2.3.4+....+98.99.100.101-98.99.97

4S=98.99.100

S=\(\frac{98.99.100}{4}\)