Question

Tính nhanh

Q=\(\frac{3}{3x5}\)+\(\frac{3}{5x7}\)+\(\frac{3}{7x9}\)+....+\(\frac{3}{47x49}\)

Answer 1

Q= 3/3x5 + 3/5x7 + 3/7x9 +...+ 3/47x49

Q= (3/3 -3/5) + (3/5-3/7) + (3/7-3/9)+...+(3/47-3/49)

Q= 3/3 - 3/5 + 3/5  - 3/7 + 3/7 -  3/9 + ... + 3/47 - 3/49

Q=3/3 - 3/49

Q= 46/49

Answer 2

72/49

Answer 3

\(\frac{23}{49}\)

Answer 4

\(Q=3\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{47.49}\right)\)

Đặt \(P=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{47.49}\)

=> \(2P=\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{47.49}\) 

=>   \(2P=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{47}-\frac{1}{49}\)

=> \(2P=\frac{1}{3}-\frac{1}{49}\Rightarrow P=\frac{46}{147}\)

=>    \(Q=3.\frac{46}{147}=\frac{46}{49}\)Vậy \(Q=\frac{46}{49}\)

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