Ta có : \(\frac{1}{2^2}< \frac{1}{1.2}\)
\(\frac{1}{3^2}< \frac{1}{2.3}\)
....
\(\frac{1}{10^2}\)< \(\frac{1}{9.10}\)
=> \(\frac{1}{2^2}+....+\frac{1}{10^2}\)< \(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{9.10}\)
=> \(\frac{1}{2^2}+....+\frac{1}{10^2}\)< \(\frac{9}{10}\)< 1
=> \(\frac{1}{2^2}+....+\frac{1}{10^2}\)< 1 ( dpcm )
Chứng tỏ rằng\(^{\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}< 1}\)
Chứng tỏ rằng:\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}< 1\)
Chứng tỏ rằng
a)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+......+\frac{1}{99^2}+\frac{1}{100^2}< \frac{3}{4}\)
b)\(4+2^2+2^3+2^4+.....+2^{10}=2^{11}.\)
Bài 6: Chứng tỏ rằng
D= \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}\)<1
Chứng tỏ rằng: \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2019^2}< \frac{3}{4}\)
Chứng tỏ rằng;
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2019^2}< \frac{3}{4}\)
Chứng tỏ rằng:
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2011^2}< \frac{3}{4}\)
a) Tìm A biết: \(A=\frac{7}{10}+\frac{7}{10^2}+\frac{7}{10^3}+...\)
b) Chứng tỏ rằng: 1/2+1/3+1/4+...+1/63>2
a)\(\frac{7}{x}<\frac{x}{4}<\frac{10}{x}\)
b) Cho A=\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{9^2}\). Chứng tỏ: \(\frac{8}{9}>A>\frac{2}{5}\)
