Question

So sánh phân số: \(\frac{2^{2014}+1}{2^{2014}}\) và \(\frac{2^{2014}+2}{2^{2014}+1}\)

nhanh lên, mk tích!

Answer 1

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

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

so sánh \(\frac{1}{2^{2014}}\) và \(\frac{1}{2^{2014}+1}\)

ta có

\(2^{2014}<2^{2014}+1\) 

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