tinh nhanh A=1/15+1/35+1/63+1/99...+1/9999
A=
49/303,xin lỗi bạn mk làm biếng viết lời giải nếu cần nói mk nha
\(A=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+........+\frac{1}{9999}\)
\(2A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+.......+\frac{2}{9999}\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+......+\frac{2}{99.101}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.......+\frac{1}{99}-\frac{1}{101}\)
\(2A=\frac{1}{3}-\frac{1}{101}\)
\(2A=\frac{98}{303}\)
\(A=\frac{98}{303}:2=\frac{98}{303}.\frac{1}{2}=\frac{49}{303}\)
49/303 { xin lỗi bạn nha mình lười không viết lời giải nếu cần thì nói cho mình biết nha }
\(A\)= \(\frac{1}{15}\)\(+\)\(\frac{1}{35}\)\(+\)\(\frac{1}{63}\)\(+\)\(\frac{1}{99}\)\(+\)........ \(+\)\(\frac{1}{9999}\)
\(A\)= \(\frac{1}{3x5}\)\(+\)\(\frac{1}{5x7}\)\(+\)\(\frac{1}{7x9}\)\(+\)\(\frac{1}{9x11}\)\(+\)......... \(+\)\(\frac{1}{99x101}\)
\(A\)= \(\left(\frac{5-3}{3x5}+\frac{7-5}{5x7}+\frac{9-7}{7x9}+.......+\frac{101-99}{99x101}\right):2\)
\(A\)= \(\left(\frac{5}{3x5}-\frac{3}{3x5}+\frac{7}{5x7}-\frac{5}{5x7}+\frac{9}{7x9}-\frac{7}{7x9}+........+\frac{101}{99x101}-\frac{99}{99x101}\right):2\)
\(A\)= \(\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.......+\frac{1}{99}-\frac{1}{101}\right):2\)
\(A\)= \(\left(\frac{1}{3}-\frac{1}{101}\right):2\)
\(A\)= \(\left(\frac{101}{303}-\frac{3}{303}\right):2\)
\(A\)= \(\frac{98}{303}:2\)
\(A\)= \(\frac{98}{303}\)x \(\frac{1}{2}\)
\(A\)= \(\frac{49}{303}\)
