\(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{94.97}\)

\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{94}-\frac{1}{97}\)

\(=1-\frac{1}{97}\)

\(=\frac{96}{97}\)

Bài làm:

Ta có: \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{94.97}\)

\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{94}-\frac{1}{97}\)

\(=1-\frac{1}{97}\)

\(=\frac{96}{97}\)

Ta có \(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{94.97}=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{94}-\frac{1}{7}=1-\frac{1}{7}=\frac{6}{7}\)

P/S : Dấu "." là dấu "x" nha !

\(S=\frac{1}{1\times4}+\frac{1}{4\times7}+\frac{1}{7\times10}+...+\frac{1}{94\times97}+\frac{1}{97\times100}\)

\(S=\frac{1}{3}\times\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{94}-\frac{1}{97}+\frac{1}{97}-\frac{1}{100}\right)\)

\(S=\frac{1}{3}\times\left(\frac{1}{1}-\frac{1}{100}\right)\)

\(S=\frac{1}{3}\times\frac{99}{100}\)

\(S=\frac{33}{100}\)

1.

=0+0-0-0+0+0-0-0+0

=0

2.

\(=2\left(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{94.97}+\dfrac{1}{97.100}\right)\)

\(=2.\dfrac{1}{3}.\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.9}+...+\dfrac{3}{97.100}\right)\)

\(=\dfrac{2}{3}.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)

\(=\dfrac{2}{3}.\left(1-\dfrac{1}{100}\right)\)

\(=\dfrac{2}{3}.\dfrac{99}{100}=\dfrac{2.99}{3.100}=\dfrac{1.33}{1.50}=\dfrac{33}{50}\)

bởi vì các số nào nhân với 0 cũng bằng 0 em ạ

hoặc dùng cách sau :

=0.(1+2-3-4+5+6-7-8+9)

=0.1

=0

1. 0,1 + 0,2 - 0,3 - 0,4 + 0,5 + 0,6 - 0,7 - 0,8 + 0,9

= ( 0,1 + 0,9 ) + ( 0,2 - 0,8 ) - ( 0,3 + 0,7 ) - ( 0,4 - 0,8 ) + 0,5

= 1 + ( - 0,6 ) - 1 - ( 0,2 ) + 0,5

= 1 + ( - 0,6 ) - 1 + 0,2 + 0,5

= [ 1 + ( - 0,6 ) ] - ( 1 - 0,2 - 0,5 )

= 0,4 - 0,3 = 0,1

`2/[1xx4]+2/[4xx7]+...+2/[97xx100]`

`=2/3xx(3/[1xx4]+3/[4xx7]+...+3/[97xx100])`

`=2/3xx(1-1/4+1/4-1/7+...+1/97-1/100)`

`=2/3xx(1-1/100)=2/3xx99/100=33/50`

\(\dfrac{2}{1.4}+\dfrac{2}{4.7}+...+\dfrac{2}{97.100}\)

\(=\dfrac{2}{3}.\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{97.100}\right)\)

\(=\dfrac{2}{3}.\dfrac{99}{100}\)

\(=\dfrac{33}{50}\)

\(\dfrac{2}{1.4}+\dfrac{2}{4.7}+...+\dfrac{2}{97.100}\)

\(=\dfrac{2}{3}.\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{97.100}\right)\)

\(=\dfrac{2}{3}.\left(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)

\(=\dfrac{2}{3}.\left(\dfrac{1}{1}-\dfrac{1}{100}\right)\)

\(=\dfrac{2}{3}.\left(\dfrac{100-1}{100}\right)\)

\(=\dfrac{2}{3}.\dfrac{99}{100}\)

\(=\dfrac{1}{1}.\dfrac{33}{50}\)

\(=\dfrac{33}{50}\)

ai yêu tui kb nha

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=24497550