Question

So sanh :
A=100¹⁰⁰+1/100⁹⁹+1 va B=100⁶⁹+1/100⁶⁸+1
Ai lam dung mik se tick

 

Answer 1

Dễ thấy A < 1. Áp dụng nếu \(\frac{a}{b}<1\) thì \(\frac{a}{b}<\frac{a+m}{b+m}\) ta có :

\(A=\frac{100^{100}+1}{100^{99}+1}<\frac{\left(100^{100}+1\right)+\left(100^{31}-1\right)}{\left(100^{99}+1\right)+\left(100^{31}-1\right)}=\frac{100^{100}+100^{31}}{100^{99}+100^{31}}=\frac{100^{31}.\left(100^{69}+1\right)}{100^{31}.\left(100^{68}+1\right)}=\frac{100^{69}+1}{100^{68}+1}=B\)

Vậy A < B

 

 

Answer 2

\(\frac{100^{100}+1}{100^{99}+1}=\frac{100^{69}+1}{100^{68}+1}\)

Answer 3

Cho hỏi vì sao?