Các câu hỏi tương tự
\(\frac{-1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-....-\frac{1}{\left(n-1\right).n}\left(n\in N\ne0,n\ne1\right)\)
Bài 2a) Aleft(frac{1}{2}-1right)left(frac{1}{3}-1right)...left(frac{1}{2002}-1right)left(frac{1}{2003}-1right)b) Bleft(-1frac{1}{2^2}right)left(-1frac{1}{3^2}right)left(-1frac{1}{4^2}right)...left(-1frac{1}{2003^2}right)left(-1frac{1}{2004^2}right)c) Cleft(1-frac{1}{2^2}right)left(1-frac{1}{3^2}right)left(1-frac{1}{4^2}right)...left(1-frac{1}{n^2}right)left(nin N,nge2right)
Đọc tiếp
Bài 2
a) \(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{2002}-1\right)\left(\frac{1}{2003}-1\right)\)
b) \(B=\left(-1\frac{1}{2^2}\right)\left(-1\frac{1}{3^2}\right)\left(-1\frac{1}{4^2}\right)...\left(-1\frac{1}{2003^2}\right)\left(-1\frac{1}{2004^2}\right)\)
c) \(C=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{n^2}\right)\left(n\in N,n\ge2\right)\)
\(\left(1-\frac{2}{2.3}\right)\left(1-\frac{2}{3.4}\right)\left(1-\frac{2}{4.5}\right)......\left(1-\frac{2}{99.100}\right)\)
Chứng minh rằng với mọi n \(\inℕ^∗\):
D = \(\frac{1}{1.2}\frac{1}{2.3}\frac{1}{3.4}+...+\frac{1}{n\left(n+1\right)}< 1\)
F = \(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{n\left(n+2\right)}\right)< 2\)
\(B=\left(1-\frac{2}{2.3}\right).\left(1-\frac{2}{3.4}\right).\left(1-\frac{2}{4.5}\right)....\left(1-\frac{2}{99.100}\right)\)
Tính A biết :
\(A=\left(1-\frac{2}{2.3}\right)\left(1-\frac{2}{3.4}\right)\left(1-\frac{2}{4.5}\right)....\left(1-\frac{2}{98.99}\right)\left(1-\frac{2}{99.100}\right)\)
tính
\(\left(1-\frac{2}{2.3}\right).\left(1-\frac{2}{3.4}\right).\left(1-\frac{2}{4.5}\right)...\left(1-\frac{2}{99.100}\right)\)
TÍNH HỢP LÝ
B=\(\left(\frac{2}{2.3}-1\right)\left(\frac{2}{3.4}-1\right)\left(\frac{2}{4.5}-1\right)...\left(\frac{2}{2008.2009}-1\right)\)
Tính tổng
S = \(\left(1-\frac{2}{2.3}\right).\left(1-\frac{2}{3.4}\right).\left(1-\frac{2}{4.5}\right).....\left(1-\frac{2}{2015.2016}\right)\)