Question

 \(S=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)

Answer 1

=> S = \(\frac{1}{3}\left(\frac{1}{1.4}+\frac{1}{4.7}+....+\frac{1}{97.100}\right)\)

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

        = \(\frac{1}{3}\left(1-\frac{1}{100}\right)=\frac{1}{3}.\frac{99}{100}=\frac{33}{100}\)

Answer 2

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

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

\(S=\frac{1}{3}.\frac{99}{100}=\frac{33}{100}\)

Answer 3

1-1/4cong 1/4 -1/7 cong.....cong 1/97-1/100

1-1/100

99/100

Answer 4

S= \(\frac{1}{1.4}\)+ \(\frac{1}{4.7}\)+,,,+ \(\frac{1}{97.100}\)

\(\Rightarrow\)S =\(\frac{1}{3}\)(1 - \(\frac{1}{4}\)+ \(\frac{1}{4}\)- \(\frac{1}{7}\)+...+ \(\frac{1}{97}\)- \(\frac{1}{100}\))

=\(\frac{1}{3}\). (1 - \(\frac{1}{100}\))

=\(\frac{1}{3}\). \(\frac{99}{100}\)

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

Answer 5

mk có cách khác nè : 

Ta có : \(S=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+....+\frac{1}{97.100}\)

\(\Rightarrow3S=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+....+\frac{3}{97.100}\)

\(\Rightarrow3S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.....+\frac{1}{97}-\frac{1}{100}\)

\(\Rightarrow3S=1-\frac{1}{100}\)

\(\Rightarrow3S=\frac{99}{100}\)

\(\Rightarrow S=\frac{99}{100}.\frac{1}{3}=\frac{33}{100}\)

Answer 6

fffffffffg đúng là óc chó

Answer 7

\(S=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\)

\(=1-\frac{1}{100}=\frac{99}{100}\)

Answer 8

S= 1/1.4+1/4.7+1/7.10+...+1/97.100

suy ra S*3=3*(1/1.4+1/4.7+....+1/97.100)

s*3=3/1.4+3/4.7+....+3/97*100

s*3=4-1/1.4+7-4/4.7+....+100-97/97.100

s*3=1/1-1/100

s*3=99/100

s=99/100:3

s=.....

vậy s=.....

Answer 9

\(S=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)

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

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

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

\(S=\frac{99}{300}=\frac{33}{100}\)

Answer 10

\(S=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)

\(< =>3S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\)

\(< =>3S=1-\frac{1}{100}=\frac{99}{100}\)

\(< =>S=\frac{99}{100}:3=\frac{33}{100}\)

Answer 11

\(S=\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{97.100}\)

\(3S=\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{97.100}\)

\(3S=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}+\frac{1}{100}\)

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

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

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

Answer 12

S = \(\frac{1}{1.4}\)+\(\frac{1}{4.7}\)+\(\frac{1}{7.10}\)+ .....+\(\frac{1}{97.100}\)

   = \(\frac{1}{3}\)\((\frac{1}{1}\)-\(\frac{1}{4}\)+\(\frac{1}{4}-\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{10}\)+ ....+\(\frac{1}{97}\)-\(\frac{1}{100})\)

   =   \(\frac{1}{3}\)\((1-\frac{1}{100}\)\()\)

   =    \(\frac{1}{3}\) . \(\frac{99}{100}\)= \(\frac{33}{100}\)

                  hok tốt

Answer 13

             Bài làm :

Ta có :

 \(S=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+....+\frac{1}{97.100}\)

\(\Rightarrow3S=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\)

\(\Leftrightarrow3S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.....+\frac{1}{97}-\frac{1}{100}\)

\(\Leftrightarrow3S=1-\frac{1}{100}\)

\(\Leftrightarrow3S=\frac{99}{100}\)

\(\Leftrightarrow S=\frac{99}{100}\div3=\frac{33}{100}\)

Vậy S=33/100