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 \(\frac{1}{10}\)+ \(\frac{1}{40}\) + \(\frac{1}{88}\) + ... + \(\frac{1}{\left(3x+2\right)\left(3x+5\right)}\) = \(\frac{4}{25}\) Giảia \(\frac{2}{2\times3}\)+ \(\frac{2}{3\times4}\) + ......
Đọc tiếp
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
Giao luu:
1.(cùng chia cho a-b)
2.cùng chia cho a
bạn sai ở chỗ cùng chia cho a-b và cùng chia cho a đó