A=\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+..+\frac{1}{9999}\)

\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+..+\frac{1}{99.101}\)

\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+..+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{101}\right)\)

\(=\frac{1}{2}.\frac{98}{303}=\frac{49}{303}\)

49/303 nha bạn

Kb với mình rồi mình giải kĩ cho

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bấm vào chữ 0 đúng sẽ ra đáp án 

A = 98/303

Cơn Mưa Tình Yêu

Đặt \(B=\frac{3}{15}+\frac{3}{35}+\frac{3}{63}+\frac{3}{99}+\frac{3}{143}\)

\(\Leftrightarrow B=\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+\frac{3}{11.13}\)

\(\Leftrightarrow2B=3\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)

\(\Leftrightarrow2B=3\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(\Leftrightarrow2B=3\left(\frac{1}{3}-\frac{1}{13}\right)=1-\frac{3}{13}=\frac{10}{13}\)

\(\Leftrightarrow A=1+\frac{3}{15}+\frac{3}{35}+\frac{3}{63}+\frac{3}{99}+\frac{3}{143}=1+\frac{10}{13}=\frac{23}{13}\)

\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{9999}\)

\(\Rightarrow\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{99.101}\)

\(\Rightarrow\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\right)\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{3}-\frac{1}{101}\right)\)

\(\Rightarrow\frac{1}{2}.\frac{98}{303}\)

\(\Rightarrow\frac{49}{303}\)

1/15 + 1/35 + 1/63 + 1/99 + ... + 1/9999 = 

= 1/(3x5) + 1/(5x7) + 1/(7x9) + ... + 1/(99x101)

= (1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ...+ 1/99 - 1/101) : 2

= (1/3 - 1/101) : 2 

= 98/303 : 2

= 49/303

\(y=\frac{1}{x^2+\sqrt{x}}\)

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

\(A=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+........+\frac{1}{9999}\)

\(2A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+.......+\frac{2}{9999}\)

\(2A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+......+\frac{2}{99.101}\)

\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.......+\frac{1}{99}-\frac{1}{101}\)

\(2A=\frac{1}{3}-\frac{1}{101}\)

\(2A=\frac{98}{303}\)

\(A=\frac{98}{303}:2=\frac{98}{303}.\frac{1}{2}=\frac{49}{303}\)

1/3 + 1/15 + 1/35 + 1/63 + 1/99 + 9999

= 1/3 + ( 1/5 + 1/35 + 1/63 ) + 1/99 = 9999

= 1/3 + 1111/9999 + 1/99

= 3333/9999 + 1111/9999 +101/9999

= 4545/9999

4546/9999

có thể giải hẳn ra được ko cái này tính máy tính cũng ra

\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...-\frac{1}{101}\)

\(A=\left(\frac{1}{3}-\frac{1}{101}\right):2\)= 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.

\(A=\frac{1}{15}+\frac{1}{35}+...+\frac{1}{9999}\)

\(A=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)

\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{99}-\frac{1}{101}\)

\(A=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)