Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(VP=1+\frac{2014}{2}+\frac{2015}{3}+...+\frac{4023}{2011}+\frac{4024}{2012}\)
\(=1-1+\left(\frac{2014}{2}-1\right)+\left(\frac{2015}{3}-1\right)+...+\left(\frac{4023}{2011}-1\right)+\left(\frac{40024}{2012}-1\right)+2012\)
\(=\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2011}+\frac{2012}{2012}+\frac{2012}{1}\)
\(=2012.\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)\)
\(\Rightarrow2012=503.x\Rightarrow x=\frac{2012}{503}=4\)
\(A=\frac{3}{1.8}+\frac{3}{8.15}+\frac{3}{15.22}+...+\frac{3}{106.113}\)
\(=\frac{3}{7}\left(\frac{7}{1.8}+\frac{7}{8.15}+\frac{7}{15.22}+...+\frac{7}{106.113}\right)\)
\(=\frac{3}{7}\left(\frac{8-1}{1.8}+\frac{15-8}{8.15}+\frac{22-15}{15.22}+...+\frac{113-106}{106.113}\right)\)
\(=\frac{3}{7}\left(1-\frac{1}{8}+\frac{1}{8}-\frac{1}{15}+\frac{1}{15}-\frac{1}{22}+\frac{1}{106}-\frac{1}{113}\right)\)
\(=\frac{3}{7}\left(1-\frac{1}{113}\right)=\frac{48}{113}\)
\(B=\frac{25}{50.55}+\frac{25}{55.60}+...+\frac{25}{95.100}\)
\(=5\left(\frac{5}{50.55}+\frac{5}{55.60}+...+\frac{5}{95.100}\right)\)
\(=5\left(\frac{55-50}{50.55}+\frac{60-55}{55.60}+...+\frac{100-95}{95.100}\right)\)
\(=5\left(\frac{1}{50}-\frac{1}{55}+\frac{1}{55}-\frac{1}{60}+...+\frac{1}{95}-\frac{1}{100}\right)\)
\(=5\left(\frac{1}{50}-\frac{1}{100}\right)=\frac{1}{20}\)
Giá trị của biểu thức đã cho là:
\(A-B=\frac{48}{113}-\frac{1}{20}=\frac{847}{2260}\)
\(\frac{2}{3}+\frac{1}{3}\left(\frac{-4}{9}+\frac{5}{6}\right)\div\frac{7}{12}\)
\(=\frac{2}{3}+\frac{1}{3}\left(\frac{-4}{9}+\frac{5}{6}\right)\times\frac{12}{7}\)
\(=\frac{2}{3}+\frac{4}{7}\left(\frac{-4}{9}+\frac{5}{6}\right)\)
\(=\frac{2}{3}+\frac{4}{7}\left(\frac{-8}{18}+\frac{15}{18}\right)\)
\(=\frac{2}{3}+\frac{4}{7}.\frac{-7}{18}\)
\(=\frac{6}{9}+\frac{-2}{9}\)
\(=\frac{4}{9}\)
\(\frac{298}{719}\div\left(\frac{1}{4}+\frac{1}{12}-\frac{1}{3}\right)-\frac{2011}{2012}\)
\(=\frac{298}{719}\div\left(\frac{3}{12}+\frac{1}{12}-\frac{4}{12}\right)-\frac{2011}{2012}\)
\(=\frac{298}{719}\div0-\frac{2011}{2012}\)
Vậy biểu thức đại số này không xác định
