\(A=\left(-\frac{1}{2}\right).\left(-\frac{2}{3}\right).\left(-\frac{3}{4}\right)......\left(-\frac{2013}{2014}\right)=\left(-\frac{1}{2014}\right)\) (Do các thừa số đều âm và A có (2014-2)+1=2013 thừa số nên A mang giá trị âm)
\(B=-\frac{1}{2015}\)
=> A<B (|A|>|B|)
Tính A = \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2014}\right)\left(1-\frac{1}{2015}\right)\left(1-\frac{1}{2016}\right)\)
bạn có thể làm câu a,b cũng được.
A)So sánh\(\frac{2014}{2015}+\frac{2015}{2014}\)và \(\frac{666665}{333333}\)
B)Tính \(\left(1-\frac{1}{28}\right)\left(1-\frac{1}{36}\right)\left(1-\frac{1}{45}\right)...\left(1-\frac{1}{1326}\right)\)
tính tích:
\(\left(1-\frac{1}{2014}\right).\left(1-\frac{2}{2014}\right).\left(1-\frac{3}{2014}\right)...\left(1-\frac{2015}{2014}\right)\)
\(y=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2014}\right)\left(1-\frac{1}{2015}\right)\)
a) Tinh: A = 4/6.10 + 6/10.16 + 1/16.3 + 1/24.7 + 1/28.5
b) Tìm 3 số tự nhiên khác nhau costoongr các nghịch đảo của chúng bằng 1 số tự nhiên.
c) So sánh A với B biết : A = \(\left(1+\frac{1}{2015}\right)\) \(\left(1+\frac{1}{2015^2}\right)\) \(\left(1+\frac{1}{2015^3}\right)\)... \(\left(1+\frac{1}{2015^{2016}}\right)\) Và B = \(\frac{2015^2-1}{2014^2-1}^{ }\)
Tính tích
\(\left(1-\frac{1}{2014}\right)\times\left( 1-\frac{2}{2014}\right)\times\left(1-\frac{3}{2014}\right).....\left(1-\frac{2015}{2014}\right)\)
Cho \(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{6}\right)....\left(1-\frac{1}{2014}\right)\)
Chung to \(A^2< \frac{1}{2015}\)
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) \(\frac{2013}{2014}+\frac{2014}{2015}+\frac{2015}{2013}>3\)
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) \(\frac{1}{2}-\frac{1}{2^2}+.........+\frac{1}{2^{99}}-\frac{1}{2^{100}}< \frac{1}{3}\)
