A=1/3-1/4+1/4-1/5+....+1/95-1/96

=1/3-1/96=31/96

1/3-1/4+1/4-1/5+1/5-1/6+......+1/95-1/96

1/3-1/96

32-1/96

31/96

\(A=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{95.96}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{95}-\frac{1}{96}\)

\(=\frac{1}{2}-\frac{1}{96}\)

\(=\frac{47}{96}\)

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47\996

hok tốt

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{95\cdot96}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{95}-\frac{1}{96}\)

\(=\frac{1}{2}-\frac{1}{96}\)

\(=\frac{47}{96}\)

\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{20}-\dfrac{1}{21}=\dfrac{1}{3}-\dfrac{1}{21}=\dfrac{6}{21}=\dfrac{2}{7}\)

\(\dfrac{2}{7}\)

6,45

\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}\\ =\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\\ =\dfrac{1}{2}-\dfrac{1}{7}\\ =\dfrac{5}{14}\)

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lèm rùi mè

=1/3 - 1/4 +1/4-1/5 +...+1/98 - 1/99

=1/3-1/99=32/99

Dễ thôi bạn!

 1/3.4+1/4.5+1/5.6+...+1/99.100

=1/3-1/4+1/4-1/5+1/5-1/6+...+1/98-1/99+1/99-1/100

=1/3-1/100

=97/300

\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)

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

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

\(=\frac{97}{300}\)

1/3.4 + 1/ 4.5 + 1/5.6 + ... + 1/99.100

= 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/99 - 1/100

= 1/3 -1/100

= 97/300

=1-1/2+1/2-1/3+......+1/5-1/6

=1-1/6

=5/6

Tick

\(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{n.\left(n+1\right)}=\dfrac{3}{10}\)

Ta có: \(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{n}-\dfrac{1}{n+1}=\dfrac{3}{10}\)

\(\dfrac{1}{3}-\dfrac{1}{x+1}=\dfrac{3}{10}\)

\(\dfrac{1}{x+1}=\dfrac{1}{3}-\dfrac{3}{10}\)

\(\dfrac{1}{x+1}=\dfrac{1}{30}\)

\(\Rightarrow x+1=30\)

\(x=30-1\)

\(x=29\)

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