Ta có :
1/3^2 < 1/2.3
1/4^2< 1/3.4
...............
1/100^2 < 1/99.100
=> 1/3^2 + 1/4^2 + ........+ 1/100^2 < 1/2.3 + 1/3.4 +.......+ 1/99.100
=> 1/3^2 + 1/4^2 +........+ 1/100^2 <1/2 - 1/3 + 1/3 - 1/4 + .........+ 1/99 - 1/100
=> 1/3^2+ 1/4^2 +........+ 1/100^2 < 1/2 - 1/100
Còn lại tự làm nhe
Chứng minh rằng: \(\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+....+\frac{1}{100^2}< \frac{1}{2}\)
Chứng minh rằng :
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}...+\frac{1}{100^2}<\frac{3}{4}\)
Chứng minh: \(\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+...+\frac{1}{100^2}<\frac{1}{2}\)
Bài 1 : Chứng minh
a) \(A=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 2\)
b) \(B=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}< 6\)
c) \(C=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}...\frac{9999}{10000}< \frac{1}{100}\)
Chứng minh rằng:
\(\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+.......+\frac{1}{100^2}<\frac{1}{2}\)
Chứng minh rằng:
\(\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+......+\frac{1}{100^2}<\frac{1}{2}\)
Chứng minh \(\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+...+\frac{1}{100^2}<\frac{1}{2}\)
Chứng minh rằng :
\(100-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}\right)=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+...+\frac{99}{100}\)
Chứng minh:
a, M= \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}< 1\)
b, \(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{4}\)
