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2A=2/3.5+2/5.7+2/7.9+...+2/99.101=>2A=1/3-1/5+1/5-1/7+...+1/99-1/100=>2A=1/3-1/100=>2A=97/300=>A=97/600
\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{9999}\)
\(\Rightarrow\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{99.101}\)
\(\Rightarrow\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\right)\)
\(\Rightarrow\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(\Rightarrow\frac{1}{2}\left(\frac{1}{3}-\frac{1}{101}\right)\)
\(\Rightarrow\frac{1}{2}.\frac{98}{303}\)
\(\Rightarrow\frac{49}{303}\)
49/303,xin lỗi bạn mk làm biếng viết lời giải nếu cần nói mk nha
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...-\frac{1}{101}\)
\(A=\left(\frac{1}{3}-\frac{1}{101}\right):2\)= 49/303
\(A=\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}+...+\frac{1}{99\times101}\)
\(=\frac{1}{2}\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+...+\frac{2}{99\times101}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{3}-\frac{1}{101}\right)\)
\(=\frac{1}{2}\times\frac{98}{303}=\frac{49}{303}\)
Vậy A = 49/303.
A=\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+..+\frac{1}{9999}\)
\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+..+\frac{1}{99.101}\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+..+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{101}\right)\)
\(=\frac{1}{2}.\frac{98}{303}=\frac{49}{303}\)
\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{99.101}\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{99.101}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\)
\(=\frac{1}{3}-\frac{1}{101}\)
\(=\frac{98}{303}\)
\(\Rightarrow A=\frac{98}{303}\div2=\frac{49}{303}\)
*Lưu ý là dấu "." là nhân nhé! Nếu bạn không chắc thì từ cái khúc 1/3 - 1/101 bạn tự làm, xong rồi chia 2 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 x 2 = \(\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{7x9}+\frac{2}{9x11}+.....+\frac{2}{99x101}\)
A x 2 = \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+.....+\frac{1}{99}-\frac{1}{101}\)
A x 2 = \(\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)
A = \(\frac{98}{303}:2=\frac{49}{303}\)
Vậy A = 49/303