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

A=1.2+1+2.3+2+3.4+3...99.100+99

A=(1.2+2.3+3.4+...99.100)+(1+2+3+4...99)

giải:

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

24497550

A=(98.99.100.101-0.1.2.3):4=242550

=348450 nha bạn

kết quả =348450 nha bạn mình được anh mình dậy

T/c:A=1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+...+1/97*98*99+1/98*99*100

2A=2/1*2*3+2/2*3*4+2/3*4*5+2/4*5*6+...+2/97*98*99+1/98*99*100

2A=(1/1*2-1/2*3)+(1/2*3-1/3*4)+(1/3*4-1/4*5)+.....+(1/97*98-1/98*99)+(1/98*99-1/99*100)

2A=1/2+1/99*100

A=tự tính nha

A= [(1/2-1/2*3)/2]+[(1/2-1/3*4)/2]+...+[(1/2-1/99*100)/2]

A=(1/2-1/99*100)/2

A=-101/198/2

A=-101/396

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

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

4A = 1.2.3.4 + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) + ... + 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 + ... + 98.99.100.101 - 97.98.99.100

4A = 98.99.100.101

=> A = 98.99.100.101 : 4

=> A = 24497550

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

\(2S=\frac{1}{2}-\frac{1}{9900}\)

\(2S=\frac{4949}{9900}\)

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

Ta xét : \(\frac{1}{1.2}-\frac{1}{2.3}=\frac{2}{1.2.3}\)

\(\frac{1}{2.3}-\frac{1}{3.4}=\frac{2}{2.3.4}\)

...

\(\frac{1}{98.99}-\frac{1}{99.100}=\frac{2}{98.99.100}\)

Ta có : 2S = \(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\)

=> 2S = \(\frac{1}{1.2}-\frac{1}{99.100}\)

=> 2S = \(\frac{4949}{9900}\)

=> S = \(\frac{4949}{19800}\)

2S=\(\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+...+\dfrac{2}{98.99.100}\)

2S= \(1-\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)2S= 1- \(\dfrac{1}{100}\)

2S= \(\dfrac{99}{100}\)

S= \(\dfrac{99}{100}.\dfrac{1}{2}\)

S=\(\dfrac{198}{100}\)

\(B=1\cdot2\cdot3+2\cdot3\cdot4+3\cdot4\cdot5+...+98\cdot99\cdot100\)

\(\Rightarrow4B=4\cdot\left(1\cdot2\cdot3+2\cdot3\cdot4+...+98\cdot99\cdot100\right)\)

\(\Rightarrow4B=1\cdot2\cdot3\cdot\left(4-0\right)+2\cdot3\cdot4\cdot\left(5-1\right)+3\cdot4\cdot5\cdot\left(6-2\right)+...+98\cdot99\cdot100\cdot\left(101-97\right)\)

\(\Rightarrow4B=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4-....+98\cdot99\cdot100\cdot101-97\cdot98\cdot99\cdot100\)

\(\Rightarrow4B=98\cdot99\cdot100\cdot101\)

\(\Rightarrow B=\dfrac{98\cdot99\cdot100\cdot101}{4}\)

\(\Rightarrow B=25\cdot98\cdot99\cdot101\)

B=1x2x3+2x3x4+...+98x99x100

=>4B=1x2x3x(4-0)+2x3x4x(5-1)+...+98x99x100x(101-97)

4B=1x2x3x4+2x3x4x5-1x2x3x4+...+98x99x100x101-97x98x99x100

4B=98x99x100x101

=>B=\(\dfrac{98\cdot99\cdot100\cdot101}{4}\)=24497550.

[1.2.3+98.99.100]x2+1=bạn tự tính nha
 

đây là bài lớp 5
 

OH MY GOD ! Bam may tinh moi het ca tay

Chắc thế!

Ta có: \(S=1\cdot2\cdot3+2\cdot3\cdot4+3\cdot4\cdot5+...+97\cdot98\cdot99\)

\(\Leftrightarrow4\cdot S=1\cdot2\cdot3\cdot\left(4-0\right)+2\cdot3\cdot4\cdot\left(5-1\right)+3\cdot4\cdot5\cdot\left(6-2\right)+...+97\cdot98\cdot99\cdot\left(101-97\right)\)

\(\Leftrightarrow4\cdot S=98\cdot99\cdot100\cdot101\)

\(\Leftrightarrow S=\text{24497550}\)

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{4.5.6}+....+\frac{1}{98.99.100}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{100}\)

\(=\frac{1}{1}-\frac{1}{100}\)

\(=\frac{99}{100}\)

=24497550

2A=\(\frac{2}{1.2.3}\)+\(\frac{2}{2.3.4}\)+\(\frac{2}{4.5.6}\)+...+\(\frac{2}{98.99.100}\)

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

2A=\(\frac{1}{1.2}\)-\(\frac{1}{99.100}\)=\(\frac{1}{2}\)-\(\frac{1}{9900}\)=\(\frac{4949}{9900}\)

A=\(\frac{4949}{9900}\):2

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