\(M=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{4005}\)
\(\frac{M}{2}=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{8010}\)
\(\frac{M}{2}=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{89x90}\)
\(\frac{M}{2}=\frac{4-3}{3.4}+\frac{5-4}{4.5}+\frac{6-5}{5.6}+...+\frac{90-89}{89.90}\)
\(\frac{M}{2}=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{89}-\frac{1}{90}=\frac{1}{3}-\frac{1}{90}\)
\(M=\frac{2}{3}-\frac{2}{90}< \frac{2}{3}\)
CHO
\(\frac{1}{M}=\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}+...+\frac{1}{1+2+3+...+59}\)
Chứng minh rằng M>\(\frac{2}{3}\)
Cho \(M=\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+59}\)
Chứng minh: M<2/3
cho:
a) A= 2+\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{62}+\frac{1}{63}+\frac{1}{64}+\frac{1}{65}+\frac{1}{66}+\frac{1}{67}\)
chứng minh rằng A>5
b) B= \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{89^2}+\frac{1}{90^2}\)
chứng minh rằng \(\frac{40}{91}\)<B<1
Cho M =\(\frac{1}{1+2+3}\)+\(\frac{1}{1+2+3+4}\)+..............................+\(\frac{1}{1+2+3+..........+59}\)
Chứng minh M<\(\frac{2}{3}\)
Cho \(M = (1+\frac{1}{2}+\frac{1}{3}+...++\frac{1}{2018}).2 .3 .4. ... .2018\)
Chứng minh : M chia hết cho 2019
\(ChoM+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+....+\frac{1}{1+2+3+4+...+59}.\)
Chứng minh rằng \(M< \frac{2}{3}\)
M=\(\frac{1}{1+2+3}\)+\(\frac{1}{1+2+3+4}\)+..............+\(\frac{1}{1+2+3+...+59}\)
chứng minh M<\(\frac{2}{3}\)
Chứng minh
M=\(\frac{1}{1+2+3}\)+\(\frac{1}{1+2+3+4}\)+\(\frac{1}{1+2+3+4+5}\)+.....+\(\frac{1}{1+2+3+....+59}\)<\(\frac{2}{3}\)
