Question

So sánh :

\(\frac{2^{2014}+1}{2^{2014}}\)

và \(\frac{2^{2014}+1}{2^{2014}+2}\)

Answer 1

ta thấy:

2^2014<2^2014+2

=>\(\frac{2^{2014}+1}{2^{2014}}>\frac{2^{2014}+1}{2^{2014}+2}\)

vậy......

Answer 2

Có : 2²⁰¹⁴ + 1 > 2²⁰¹⁴ nên \(\frac{2^{2014}+1}{2^{2014}}\)> 1 .

2²¹⁰⁴ + 1 < 2²⁰¹⁴ + 2 nên \(\frac{2^{2014}+1}{2^{2014}+2}\)< 1.

=> \(\frac{2^{2014}+1}{2^{2014}}\)>\(\frac{2^{2014}+1}{2^{2014}+2}\)

Answer 3

1 cách dễ hơn nè:

Có 2²⁰¹⁴+1 = 2²⁰¹⁴ + 1 ( tử và tử bằng nhau )

2²⁰¹⁴<2²⁰¹⁴+2

=>\(\frac{2^{2014}+1}{2^{2014}}>\frac{2^{2014}+1}{2^{2014}+2}\)