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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
Dãy số trên có tất cả số 1 là :
[ ( 96 - 1 ) : 1 + 1 ] : 2 = 48 ( số )
TA có :
( 1 + 1 + 1 + ... + 1 ) + \(\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{95.96}\right)\)
= 48 + \(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{95}-\frac{1}{96}\right)\)
= 48 + \(\left(1-\frac{1}{96}\right)\)
= 48 + \(\frac{95}{96}\)
= \(48\frac{95}{96}\)
TK nha !
d, `3,15+2,4=5,55`
e, \(\dfrac{5}{7}.\dfrac{2}{11}+\dfrac{5}{7}.\dfrac{9}{11}=\dfrac{5}{7}\left(\dfrac{2}{11}+\dfrac{9}{11}\right)=\dfrac{5}{7}.\dfrac{11}{11}=\dfrac{5}{7}.1=\dfrac{5}{7}\)
f, `1,25.3,6+3,6.8,75=3,6(1,25+8,75)=3,6.10=36`
\(h,\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\\ =1-\dfrac{1}{100}\\ =\dfrac{99}{100}\)
\(e\dfrac{5}{7}\times\left(\dfrac{2}{11}+\dfrac{9}{11}\right)=\dfrac{5}{7}\times1=\dfrac{5}{7}\)
\(f3.6\times\left(1.25+8.75\right)=3.6\times10=36\)
1/2.3+1/3.4+1/4.5+...+1/99.100
=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{99}-\frac{1}{100}\)
=\(\frac{1}{2}-\frac{1}{100}=\frac{50}{100}-\frac{1}{100}=\frac{49}{100}\)
=1/2-1/3+1/3-1/4+1/4-1/5+......+1/99-1/100
=1/2-1/100
=49/100
1/2*3+1/3*4+...+1/99*100
=1/2-1/3+1/3-1/4+...+1/99-1/100
=50/100-1/100=49/100
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
\(A=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{25\cdot26}\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{25}-\frac{1}{26}\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{26}\)
\(\Rightarrow A=\frac{12}{26}=\frac{6}{13}\)
\(A=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{95.96}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{95}-\frac{1}{96}\)
\(=\frac{1}{2}-\frac{1}{96}\)
\(=\frac{47}{96}\)
>.<
47\996
hok tốt