Question

Tìm X

2/1x3 + 2/3x5 + 2/5x7 +...+2/X x(X+2) =101/102

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Answer 1

\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{101}{102}\)

\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{101}{102}\)

\(1-\frac{1}{x+2}=\frac{101}{102}\)

\(1-\frac{1}{x+2}=1-\frac{1}{102}\)

\(\frac{1}{x+2}=\frac{1}{102}\)

x+2=102

x=102-2

x=100

Answer 2

2/1x3 + 2/3x5 + 2/5x7 + ... + 2/Xx(X+ 2 ) = 101/102

1/1 - 1/3 + 1/3 - 1/5  + 1/5 - 1/7 + .. + 1/x - 1/x + 2 = 101/102

1 - 1/x + 2 = 101/102

1 - 1/x + 2 = 1 - 1/102

1/x + 2 = 1/102

x + 2 =102

x = 102 - 2

x = 100

Chúc bạn học tốt!

Answer 3

2/1x3 + 2/3x5 + 2/5x7 + ... + 2/Xx(X+ 2 ) = 101/102

1/1 - 1/3 + 1/3 - 1/5  + 1/5 - 1/7 + .. + 1/x - 1/x + 2 = 101/102

1 - 1/x + 2 = 101/102

1 - 1/x + 2 = 1 - 1/102

1/x + 2 = 1/102

x + 2 =102

x = 102 - 2

x = 100

Chúc bạn học tốt!

Answer 4

\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{101}{102}\)

\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{101}{102}\)

\(1-\frac{1}{x+2}=\frac{101}{102}\)

\(\frac{1}{x+2}=\frac{1}{102}\)

x+2=102

x=102-2

x=100

Answer 5

x=100