Question

M=\(\dfrac{1}{1.5}\)+\(\dfrac{2}{5.13}\)+\(\dfrac{3}{12.25}\)+\(\dfrac{4}{25.41}\) và N=\(\dfrac{2}{1.7}\)+ \(\dfrac{3}{7.16}\)+\(\dfrac{4}{16.28}\)+\(\dfrac{5}{28.43}\)+\(\dfrac{6}{43.61}\)

so sánh M và N

Answer 1

M=1/4(4/1*5+8/5*13+...+16/25*41)

=1/4(1-1/5+1/5-1/13+...+1/25-1/41)

=40/41*1/4=10/41

\(N=\dfrac{1}{3}\left(1-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{16}+...+\dfrac{1}{43}-\dfrac{1}{61}\right)=\dfrac{1}{3}\cdot\dfrac{60}{61}=\dfrac{20}{61}\)

=>M<N