CM \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}\)<\(\frac{3}{4}\)
A=\(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{99.100}\)CM \(\frac{7}{12}< A< \frac{5}{6}\)
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:
a/\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\)
b/\(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}< 1\frac{3}{4}\)
c/\(\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+...+\frac{1}{100^2}< \frac{1}{2}\)
Cho A=\(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}\)
B=\(\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\)
CM A<B
b, Cm A <\(\frac{1}{10}\)
Bài 1: Chứng minh rằng:
1)\(\frac{1}{5}< A=\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2007^2}\)
2)\(B=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{81}+\frac{1}{100}>\frac{65}{132}\)
3)\(C=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{3}{4}\)
4)\(\frac{1}{6}< D=\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}\)
5)\(E=\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+...+\frac{1}{100^2}< \frac{1}{4}\)
Bài 2 : Cho \(D=\frac{12}{\left(2\cdot4\right)^2}+\frac{20}{\left(4\cdot6\right)^2}+...+\frac{388}{\left(96\cdot98\right)^2}+\frac{396}{\left(98\cdot100\right)^2}\)
Hãy so sánh\(D\) với \(\frac{1}{4}\)
Cảm ơn các bạn nhiều!
a, A=\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}< 1\)
b, B=\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{99.100}< 2\)
c, C=\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{63}< 6\)
d, D=\(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}....\frac{9999}{10000}< \frac{1}{100}\)
a) \(A=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2014^2}< 2^{ }\)
b)\(B=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}< 6\)
c)\(C=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{9999}{10000}< \frac{1}{100}\)
1)Chứng minh các phân số sau là các phân số tối giản:
a)\(A=\frac{12n+1}{30n+2}\)
b)\(B=\frac{14n+17}{21n+25}\)
2)Chứng minh rằng:
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)\(C=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{9999}{10000}< \frac{1}{100}\)
cm
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=\(\frac{1}{2}\).\(\frac{3}{4}\).\(\frac{5}{6}\).\(\frac{7}{8}\)...\(\frac{9999}{10000}\)<\(\frac{1}{100}\)