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a. \(\frac{34\times34}{33\times35}\)
\(=\frac{34\times33+34}{33\times34+33}\)
Vì \(34>33\)nên Tử > Mẫu
\(\Rightarrow\frac{34\times34}{33\times35}>1\)
b. \(\frac{1991\times1999}{1995\times1995}\)
\(=\frac{1991\times\left(1995+4\right)}{1995\times\left(1991+4\right)}\)
\(=\frac{1991\times1995+1991\times4}{1995\times1991+1995\times4}\)
Vì \(1995\times4>1991\times4\)nên Tử > Mẫu
\(\Rightarrow\frac{1991\times1999}{1995\times1995}>1\)
Ta có:
\(\frac{1}{5}=\frac{1}{5};\frac{1}{6}<\frac{1}{5};\frac{1}{7}<\frac{1}{5};\frac{1}{8}<\frac{1}{5};\frac{1}{9}<\frac{1}{5}\)
Nên\(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}<\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}=\frac{5}{5}=1\)
Vậy A<1
A=1995*1995 B=1994*1996
A=(1994+1)*1995 B=1994*(1995+1)
A=1994*1995+1*1995 B=1994*1995+1*1994
Vì 1994*1995=1994*1995 ; 1*1995 > 1*1994
Nên 1995*1995 > 1994*1996
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>1/4+1/4+1/16+1/16+1/16
=2/4+3/16=11/16=66/96<80/96=5/6
vậy A<5/6
=1/2.(1+1/3+1/6+...+1/45)
=1/2+1/6+1/12+1/20+...+1/90
=1/1.2+1/2.3+1/3.4+...+1/9.10
=(1/1-1/2)+(1/2-1/3)+...+(1/9-1/10)
=1-1/10
=9/10
dung do..k hegg
ban lam giups bai nay nhe:
tính tổng của 1/11 + 1/12 + 1/13 + ... +1/30 rồi so sánh a với 2/3