Các câu hỏi tương tự
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 :
\(100-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}\right)=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+...+\frac{99}{100}\)
chứng minh:
B=\(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}< 6\)
C=\(1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 2\)
1)Chứng minh các phân số sau là các phân số tối giản:a)Afrac{12n+1}{30n+2}b)Bfrac{14n+17}{21n+25}2)Chứng minh rằng:a)A1+frac{1}{2^2}+frac{1}{3^2}+frac{1}{4^2}+...+frac{1}{100^2} 2b)B1+frac{1}{2}+frac{1}{3}+frac{1}{4}+...+frac{1}{63} 6c)Cfrac{1}{2}.frac{3}{4}.frac{5}{6}.....frac{9999}{10000} frac{1}{100}
Đọc tiếp
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)\(C=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{9999}{10000}< \frac{1}{100}\)
Chứng tỏ rằng
a) \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\)
b) \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2018^2}< \frac{3}{4}\)
c) \(\frac{1}{3}+\frac{3}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}< \frac{3}{4}\)
Bài 1: Chứng minh rằng:1)frac{1}{5} Afrac{1}{5^2}+frac{1}{6^2}+frac{1}{7^2}+...+frac{1}{2007^2}2)Bfrac{1}{4}+frac{1}{9}+frac{1}{16}+...+frac{1}{81}+frac{1}{100}frac{65}{132}3)Cfrac{1}{2^2}+frac{1}{3^2}+frac{1}{4^2}+...+frac{1}{100^2} frac{3}{4}4)frac{1}{6} Dfrac{1}{5^2}+frac{1}{6^2}+frac{1}{7^2}+...+frac{1}{100^2}5)Efrac{1}{4^2}+frac{1}{6^2}+frac{1}{8^2}+...+frac{1}{100^2} frac{1}{4}Bài 2 : Cho Dfrac{12}{left(2cdot4right)^2}+frac{20}{left(4cdot6right)^2}+...+frac{388}{left(96cdot98right)^2}+frac...
Đọc tiếp
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!
Chứng minh frac{1}{5}+frac{1}{13}+frac{1}{14}+frac{1}{15}+frac{1}{61}+frac{1}{62}+frac{1}{63} frac{1}{2}frac{1}{2}b,frac{1}{^{2^2}}+frac{1}{4^2}+frac{1}{6^2}+...+frac{1}{100^2} frac{1}{2}c,frac{3}{4}+frac{8}{9}+frac{15}{16}+...+frac{2499}{2500}48d,frac{1}{6} frac{1}{5^2}+frac{1}{6^2}+frac{1}{7^2}+...+frac{1}{100^2} frac{1}{4}
Đọc tiếp
Chứng minh \(\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{2}\)\(\frac{1}{2}\)
b,\(\frac{1}{^{2^2}}+\frac{1}{4^2}+\frac{1}{6^2}+...+\frac{1}{100^2}< \frac{1}{2}\)
c,\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}>48\)
d,\(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{4}\)
Chứng minh
100-(1-\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}\))= \(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{99}{100}\)
Chứng minh rắng
a) \(\frac{1}{2}+\frac{2}{2^2}+\frac{3}{2^3}+..+\frac{100}{2^{100}}<2\)
b) \(\frac{4}{3}<\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+..+\frac{1}{70}<\frac{5}{2}\)
c) \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}<\frac{3}{4}\)