Các câu hỏi tương tự
Tìm n biết:
\(\frac{1}{2}\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{n\left(n+2\right)}\right)=\frac{2013}{2014}\)
Với \(n\in\)N*
cmr\(B=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)....\left(1+\frac{1}{n\left(n+2\right)}\right)< 2\)
Tìm n biết \(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)...\left(1+\frac{1}{\left(n-1\right)\left(n+1\right)}\right)=1\frac{1007}{1008}\)
Tìm n biết: \(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right)...\left(1+\frac{1}{\left(n-1\right)\left(n+1\right)}\right)=1\frac{1007}{1008}\)
Tìm n biết : \(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)...\left(1+\frac{1}{1.\left(n+1\right)}\right)=1\frac{1007}{1008}\)
c) a(x + 5) . ( n - 8 ) = 1
b) \(\frac{1}{2}.2^n=2^1.3^2.4^2-4.2^n\)
:)) giúp mk với lm ơn :))
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 = \(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{n\left(n+2\right)}\right)< 2\)
Cho tích P = ( 1+\(\frac{1}{1.3}\)) ( 1+\(\frac{1}{2.4}\)) ... [ 1+\(\frac{1}{n\left(n+2\right)}\)] . Tìm các số nguyên dương n để 3P \(\inℤ\)
Tìm số tự nhiên n biết :
\(2.2^2+3.2^3+4.2^4+...+\left(n-1\right).2^{n-1}+n.2^n=2^{n+34}\)