1/5^2< 1/4.5=1/4-1/5
1/6^2<1/5.6=1/5-1/6
..
1/99^2<1/98.99=1/98-1/99
1/100^2<1/99.100=1/99-1/100
Cộng vế theo vế
=> 1/5^2+1/6^2+...+1/100^2< 1/4 -1/100<1/4
1/5^2> 1/5.6=1/5-1/6
1/6^2>1/6.7=1/6-1/7
..
1/99^2>1/99.100=1/99-1/100
1/100^2>1/100.101=1/100-1/101
Cộng vế theo vế
=> 1/5^2+1/6^2+...+1/100^2>1/5 -1/101=96/505>1/6
CMR : \(\frac{1}{6}
CMR:\(\frac{1}{6}<\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+.....+\frac{1}{100^2}<\frac{1}{4}\)
CMR:\(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\)\(\frac{1}{100^2}< \frac{1}{4}\)
giúp mk với các bn . CMR \(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+..+\frac{1}{100^2}< \frac{1}{4}\)
Cho A=\(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}\)
CMR \(\frac{1}{6}< A< \frac{1}{4}\)
CMR :
a) \(\frac{1}{3}+\frac{1}{31}+\frac{1}{35}+\frac{1}{37}+\frac{1}{47}+\frac{1}{53}+\frac{1}{61}< \frac{1}{2}\)
b) \(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+....+\frac{1}{100^2}< \frac{1}{4}\)
CMR :
\(\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{99}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{100}\right)\)
\(=\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+\frac{1}{100}\)
\(\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+...+\frac{1}{100^2}< \frac{1}{2}\)
CMR :tổng trên bé hơn \(\frac{1}{2}\)
a. CMR \(\frac{1}{6}<\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}<\frac{1}{4}\)
b.Tìm số nguyên a để : \(\frac{2a+9}{a+3}+\frac{5a+17}{a+3}-\frac{3a}{a+3}\) là số nguyên