Đặt A = \(\frac{1}{2}+\frac{1}{2.2}+\frac{1}{2.2.2}+....+\frac{1}{2.2.2.2.2.2.2.2.2.2}\)
=> A = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{10}}\)
=> 2A = \(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^9}\)
=> 2A - A = \(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^9}-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)
=> A = \(1-\frac{1}{2^{10}}\)
Let a,b,c,d,e are integers satisfying the following expression:
\(\frac{501}{2015}\)=\(\frac{1}{a+\frac{1}{b+\frac{1}{c+\frac{1}{d+\frac{1}{e}}}}}\)
Find the value of a+b+c+d+e
Toán tiếng anh,giải giúp mik
Find the sum of 100 the first term of the sequence.
\(\frac{1}{6};\frac{1}{60};\frac{1}{176};\frac{1}{136};...\)
chung to :C = \(\frac{1}{1.1!}+\frac{1}{2.2!}+\frac{1}{3.3!}+...+\frac{1}{2019.2019!}< \frac{3}{2}\)
a)\(\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}=\frac{x+1}{5}+\)\(\frac{x+1}{6}\)
b)\(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\)\(\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}\)
c)\(2.2^2.2^3.2^4.........2^x=1024\)\(\left(x\in z\right)\)
Tìm x
S=\(\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+\frac{1}{5.5}+...+\frac{1}{49.49}+\frac{1}{50.50}\)=?
chung minh
\(\frac{1}{2.2}+\frac{1}{2.3}+...+\frac{1}{2013}+\frac{1}{2013}\)
chứng minh rằng : \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+....+\frac{19}{9^2.10^2}< 1\)
CMR\(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+....+\frac{19}{9^2.10^2}<1\)
CMR\(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}<1\)
