Question

so sánh : N=\(\frac{-7}{10^{2005}}+\frac{-15}{10^{2006}}vàM=\frac{-15}{10^{2005}}+\frac{-7}{10^{2006}}\)

Answer 1

Xét N ta có :

N = \(\frac{-7}{10^{2005}}\)+ \(\frac{-15}{10^{2006}}\)

N = \(\frac{-7}{10^{2005}}\)+ \(\frac{-7}{10^{2006}}\)+\(\frac{-8}{10^{2006}}\)

Xét M ta có :

M = \(\frac{-15}{10^{2005}}\)+\(\frac{-7}{10^{2006}}\)

M = \(\frac{-8}{10^{2005}}\)+\(\frac{-7}{10^{2005}}\)+ \(\frac{-7}{10^{2006}}\)

Vì \(\frac{-8}{10^{2006}}\)< \(\frac{-8}{10^{2005}}\) => N < M

Answer 2

Khó V~

Answer 3

ta có:M-N=\(\dfrac{-15}{10^{2005}}-\dfrac{-7}{10^{2005}}+\dfrac{-7}{10^{2006}}-\dfrac{-15}{10^{2006}}\)

=\(\dfrac{-8}{10^{2015}}\)+\(\dfrac{8}{10^{2016}}\)=8(\(\dfrac{1}{10^{2006}}-\dfrac{1}{10^{2005}}\))

Ta có:10²⁰⁰⁶>10²⁰⁰⁵<=>\(\dfrac{1}{10^{2006}}< \dfrac{1}{10^{2005}}\)

<=>\(\dfrac{1}{10^{2006}}-\dfrac{1}{10^{2005}}< 0\)

=>M-N<0 hay N>M