Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
B = \(\frac{1}{1+\frac{1}{2}}+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}+\frac{1}{1+\frac{1}{3}}\)
B = \(\frac{1}{\frac{2}{2}+\frac{1}{2}}+\frac{1}{1+\frac{1}{\frac{2}{2}+\frac{1}{2}}}+\frac{1}{\frac{3}{3}+\frac{1}{3}}\)
B = \(\frac{1}{\frac{3}{2}}+\frac{1}{1+\frac{1}{\frac{3}{2}}}+\frac{1}{\frac{4}{3}}\)
B = \(\frac{2}{3}+\frac{1}{1+\frac{2}{3}}+\frac{3}{4}\)
B = \(\frac{2}{3}+\frac{1}{\frac{3}{3}+\frac{2}{3}}+\frac{3}{4}\)
B = \(\frac{2}{3}+\frac{1}{\frac{5}{3}}+\frac{3}{4}\)
B = \(\frac{2}{3}+\frac{3}{5}+\frac{3}{4}\)
B = \(\frac{121}{60}\)
cái này tính từng phân số theo quy luật từ dưới lên trên rồi tính B là ra
Đặt \(B=\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{2014^2}\)
Ta có : \(\frac{1}{3^2}< \frac{1}{2.3}\)
\(\frac{1}{4^2}< \frac{1}{3.4}\)
\(\frac{1}{5^2}< \frac{1}{4.5}\)
...
\(\frac{1}{2014^2}< \frac{1}{2013.2014}\)
\(\Rightarrow B< \frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2013.2014}\)
\(\Rightarrow B< \frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2013}-\frac{1}{2014}\)
\(\Rightarrow B< \frac{1}{2}-\frac{1}{2014}< \frac{1}{2}\)
\(\Rightarrow A< \frac{1}{2^2}+\frac{1}{2}=\frac{3}{4}\)
Vậy A<\(\frac{3}{4}\)
A<\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\)=\(\frac{2013}{2014}\)<\(\frac{3}{4}\)
\(\frac{3-x}{5-x}=\left(\frac{3}{5}\right)^2\)
\(\Rightarrow\frac{3-x}{5-x}=\frac{9}{25}\)
\(\Rightarrow\left(3-x\right)25=9\left(5-x\right)\)
\(\Rightarrow75-25x=45-9x\)
\(\Rightarrow-25x+9x=45-75\)
\(\Rightarrow-16x=-30\)
\(\Rightarrow x=\frac{15}{8}\)
\(4\frac{2}{7}.3=\left(4+\frac{2}{7}\right).3=4.3+\frac{2}{7}.3=12+\frac{6}{7}=12\frac{6}{7}\)
Cách này nhanh hơn nhiều đúng không
Ta có:\(\frac{16}{25}\)+ (x+\(\frac{1}{3}\))\(^2\)=1
(x+\(\frac{1}{3}\))\(^2\)= \(\frac{9}{25}\)
x+\(\frac{1}{3}\)= \(\frac{3}{5}\)
x=\(\frac{4}{15}\)
\(\frac{16}{25}+\left(x+\frac{1}{3}\right)^2=1\)
\(\left(x+\frac{1}{3}\right)^2=1-\frac{16}{25}\)
\(\left(x+\frac{1}{3}\right)^2=\frac{9}{25}=0,36\)
\(x+\frac{1}{3}=0,6=\frac{3}{5}\)
\(x=\frac{3}{5}-\frac{1}{6}\)
\(x=\frac{13}{30}\)