tìm x:

a,\(\frac{x}{2\times5}+\frac{x}{5\times8}+\frac{x}{8\times11}+\frac{x}{11\times14}=\frac{3}{7}\)

b, \(50\%+\frac{2}{3}x=x+4\)

c,\(0,5x-\frac{2}{3}\left(x+1\right)=\frac{-1}{12}\)

d,\(\frac{1}{2}\left(x-\frac{2}{3}\right)-\frac{2}{5}\left(2-x\right)=\frac{1}{9}\)

Tìm x\(\in\)Z biết :

a \(\frac{2}{2\times3}\)+ \(\frac{2}{3\times4}\)+ \(\frac{2}{4\times5}\)+  ... + \(\frac{2}{X\left(X+1\right)}\) = \(\frac{2007}{2009}\)

b \(\frac{1}{10}\)+ \(\frac{1}{40}\) + \(\frac{1}{88}\) + ... +  \(\frac{1}{\left(3x+2\right)\left(3x+5\right)}\) = \(\frac{4}{25}\)

                                                                                  Giải

a \(\frac{2}{2\times3}\)+ \(\frac{2}{3\times4}\) + ... + \(\frac{2}{x\left(x-1\right)}\)= \(\frac{2007}{2009}\)

\(\Leftrightarrow\)2(\(\frac{1}{2}\) \(-\) \(\frac{1}{3}\) + \(\frac{1}{3}\) \(-\)\(\frac{1}{4}\) + ... + \(\frac{1}{x}\) \(-\) \(\frac{1}{x+1}\))  = \(\frac{2007}{2009}\) \(\Leftrightarrow\)\(\frac{1}{2}\) \(-\)\(\frac{1}{x+1}\)= \(\frac{2007}{4018}\)

\(\Leftrightarrow\)\(\frac{1}{x+1}\)= \(\frac{1}{2}\)\(-\)\(\frac{2007}{4018}\) \(\Leftrightarrow\) \(\frac{1}{x+1}\) =\(\frac{1}{2009}\)\(\Leftrightarrow\)x + 1 = 2009 \(\Leftrightarrow\)x = 2008

b \(\frac{1}{10}\) + \(\frac{1}{40}\) + \(\frac{1}{88}\) + ... + \(\frac{1}{\left(3x+2\right)\left(3x+5\right)}\)= \(\frac{4}{25}\)

\(\Leftrightarrow\) \(\frac{1}{2\times5}\) + \(\frac{1}{5\times8}\) + \(\frac{1}{8\times11}\) + ... + \(\frac{1}{\left(3x+2\right)\left(3x+5\right)}\) = \(\frac{4}{25}\)

\(\Leftrightarrow\) \(\frac{1}{3}\)(\(\frac{3}{2\times5}\) + \(\frac{3}{5\times8}\) + \(\frac{3}{8\times11}\) + ... + \(\frac{3}{\left(3x+2\right)\left(3x+5\right)}\) ) = \(\frac{4}{25}\)

\(\Leftrightarrow\) \(\frac{1}{3}\)(\(\frac{1}{2}\)\(-\)\(\frac{1}{5}\) + \(\frac{1}{5}\) \(-\)\(\frac{1}{8}\)+ ...+  \(\frac{1}{3x+2}\) \(-\)\(\frac{1}{3x+5}\)) =  \(\frac{4}{25}\)\(\Leftrightarrow\)\(\frac{1}{2}\)\(-\)\(\frac{1}{3x+5}\)=\(\frac{12}{25}\)

\(\Leftrightarrow\)\(\frac{1}{3x+5}\) =\(\frac{1}{2}\)\(-\)\(\frac{12}{25}\) \(\Leftrightarrow\) 3x + 5 = 50 \(\Leftrightarrow\)3x = 45 \(\Leftrightarrow\) x = 15                                                                    Các bạn có cách làm giống mình thì trả lời nhé               

Tính giá trị của các biểu thức bằng cách hợp lí

a/\(\frac{-8}{18}\)-\(\frac{15}{27}\)

b/\(\frac{19}{24}\)- ( \(\frac{-1}{2}\)\(+\)\(\frac{7}{24}\))

c/ P=\(\frac{3^{11}\times11+3^{11}\times21}{3^9\times2^5}\)

d/\(\frac{2}{1\times2}\)\(+\)\(\frac{2}{2\times3}\)\(+\)\(\frac{2}{3\times4}\)\(+\)... \(+\)\(\frac{2}{99\times100}\)

C1.  Tìm \(\frac {a}b\), biết rằng :

a, \(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}\)

b, \(B=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}\)

c, \(C=\frac{1}{1\cdot2\cdot3\cdot4}+\frac{1}{2\cdot3\cdot4\cdot5}+...+\frac{1}{27\cdot28\cdot29\cdot30}\)

C2. Tìm x :

1. \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{\frac{x\left(x+1\right)}{2}}=1\frac{1991}{1993}\)

2. \(\frac{1}{5\times8}+\frac{1}{8\times11}+...+\frac{1}{11\times14}+...+\frac{1}{x\times(x+3)}=\frac{101}{1540}\)

Tính giá trị biểu thức sau :

a) A= -2 \(\frac{1}{2}\): (\(\frac{-1}{2}\))^2 - \(\frac{1}{-3}\)*(\(\frac{-1}{2}\)-\(\frac{4}{3}\):\(\frac{-8}{9}\))

b) B = ( 3\(\frac{10}{99}\)+ 4\(\frac{11}{99}\)- 5\(\frac{8}{299}\))* (\(\frac{1}{2}\)- \(\frac{1}{3}\)-\(\frac{1}{6}\))

Bài này là bài HSG lớp 6 mik ko giải được ... Giaỉ giúp mik nha :p

Bài 1:Tính tổng 50 số hạng đầu tiên của dãy:

a)\(\frac{2}{3\times4}\); \(\frac{2}{4\times5}\);\(\frac{2}{5\times6}\);.......

b)\(\frac{1}{6}\);\(\frac{1}{12}\);\(\frac{1}{20}\);\(\frac{1}{30}\);......

c)\(\frac{3}{3}\);\(\frac{3}{15}\);\(\frac{3}{35}\);\(\frac{3}{63}\);......

Tính hợp lí :

\(\frac{1}{7}.\frac{1}{3}+\frac{1}{7}.\frac{1}{2}-\frac{1}{7}\)

Rút gọn rồi tính :

1) \(\frac{5^4\times9^5}{15^3\times27^3}\)

2) \(\frac{8^8\times3^{14}}{9^6\times2^{20}}\)

3) \(\frac{4^{10}\times25^7}{5^{14}\times8^6}\)

4) \(\frac{25^7\times2^{15}}{8^5\times5^{12}}\)

1.\(ChoA=\frac{3n+5}{n+1\left(n\inℤ\right)}\)

a.Tìm n để A là phân số

b.Tìm n thuộc Z để A có giá trị nguyên

c.Tìm n thuộc N để A tối giản.

2.So sánh:

a.\(\frac{97}{100}\)và  \(\frac{95}{98}\)

b.A = \(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\)và \(1\)

c.A=\(\frac{10^{2015}+1}{10^{2017}+1}\)và  B= \(\frac{10^{2017}+1}{10^{2019}+1}\)