Question

So sánh:

A=\(\frac{10^{2014}+1}{10^{2015}+1}\)      và  B=\(\frac{10^{2015}+1}{10^{2016}+1}\)

Answer 1

xét A ta có 

\(10A=\frac{10.\left(10^{2014}+1\right)}{10^{2015}+1}=\frac{10^{2015}+10}{10^{2015}+1}=\frac{\left(10^{2015}+1\right)+9}{10^{2015}+1}\)suy ra \(10A=1+\frac{9}{10^{2015}+1}\)

xét B ta có 

\(10B=\frac{10.\left(10^{2015}+1\right)}{10^{2016}+1}=\frac{10^{2016}+10}{10^{2016}+1}=\frac{\left(10^{2016}+1\right)+9}{10^{2016}+1}=1+\frac{9}{10^{2016}+1}\)

Vì 10A>10B suy ra A >B

 

Answer 2

10A = 10 2015 + 1 10. 10 2014 + 1

= 10 2015 + 1 10 2015 + 10

= 10 2015 + 1 10 2015 + 1 + 9

suy ra 10A = 1 + 10 2015 + 1 9 

Answer 3

10A=10.(102014+1102015+1 )=102015+10102015+1 =102015+1+9102015+1 =1+9102015+1 

10B=10.(102015+1102016+1 )=102016+10102016+1 =102016+1+9102016+1 =1+9102016+1 

Vì 1 = 1; 9 = 9 ta so sánh mẫu:

Ta có: 10²⁰¹⁵ < 10²⁰¹⁶ => 10²⁰¹⁵+1 < 10²⁰¹⁶+1

=> 1+9102015+1 >1+9102016+1 

=> 10A > 10B

=> A > B.

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