Các câu hỏi tương tự
\(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)....\left(\frac{1}{2013^2}-1\right).\left(\frac{1}{2014^2}-1\right)\)
\(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)....\left(\frac{1}{2013^2}-1\right).\left(\frac{1}{2014^2}-1\right)\)=?
\(A=\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)\left(\frac{1}{4^2}-1\right).....\left(\frac{1}{2013^2}-1\right)\left(\frac{1}{2014^2}-1\right)\)
CHỨNG TỎ : A<-1/2
Cho \(A=\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{2013^2}-1\right)\left(\frac{1}{2014^2}-1\right)\)
Và B =\(\frac{1}{2}\)
So sánh A và B
Chứng tỏ:a) frac{2013}{2014}+frac{2014}{2015}+frac{2015}{2013}3b) left(1+frac{1}{2}right)left(1+frac{1}{2^2}right)left(1+frac{1}{2^3}right)left(1+frac{1}{2^4}right)....left(1+frac{1}{2^{50}}right) 3c) Cfrac{1}{2}.frac{3}{4}.frac{5}{6}.....frac{9999}{10000} frac{1}{100}d) frac{1}{2}-frac{1}{2^2}+.............+frac{1}{2^{99}}-frac{1}{2^{100}} frac{1}{3}
Đọc tiếp
Chứng tỏ:
a) \(\frac{2013}{2014}+\frac{2014}{2015}+\frac{2015}{2013}>3\)
b) \(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{2^2}\right)\left(1+\frac{1}{2^3}\right)\left(1+\frac{1}{2^4}\right)....\left(1+\frac{1}{2^{50}}\right)< 3\)
c) \(C=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{9999}{10000}< \frac{1}{100}\)
d) \(\frac{1}{2}-\frac{1}{2^2}+.............+\frac{1}{2^{99}}-\frac{1}{2^{100}}< \frac{1}{3}\)
Chứng tỏ:a) frac{2013}{2014}+frac{2014}{2015}+frac{2015}{2013}3b) left(1+frac{1}{2}right)left(1+frac{1}{2^2}right)left(1+frac{1}{2^3}right)left(1+frac{1}{2^4}right)...left(1+frac{2}{50}right) 3c) Cfrac{1}{2}.frac{3}{4}.frac{5}{6}.....frac{9999}{10000} frac{1}{100}d) frac{1}{2}-frac{1}{2^2}+.........+frac{1}{2^{99}}-frac{1}{2^{100}} frac{1}{3}
Đọc tiếp
Chứng tỏ:
a) \(\frac{2013}{2014}+\frac{2014}{2015}+\frac{2015}{2013}>3\)
b) \(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{2^2}\right)\left(1+\frac{1}{2^3}\right)\left(1+\frac{1}{2^4}\right)...\left(1+\frac{2}{50}\right)< 3\)
c) \(C=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.....\frac{9999}{10000}< \frac{1}{100}\)
d) \(\frac{1}{2}-\frac{1}{2^2}+.........+\frac{1}{2^{99}}-\frac{1}{2^{100}}< \frac{1}{3}\)
Cho \(A=\left(\frac{1}{^{2^2}}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)......\left(\frac{1}{2013^2}-1\right).\left(\frac{1}{2014^2}-1\right)va\)\(B=-\frac{1}{2}.\)Hay so sanh A va B
Tính nhanh
A = \(\left(\frac{2014}{2}+\frac{2014}{3}+\frac{2014}{4}+...+\frac{2014}{2015}\right):\left(\frac{2014}{1}+\frac{2013}{2}+\frac{2012}{3}+...+\frac{1}{2014}\right)\)
\(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{2013^2}-1\right).\left(\frac{1}{2014^1}-1\right)\)
Hãy chứng minh : \(A<-\frac{1}{2}\)