Question

C= \(\frac{3}{3\times5}+\frac{3}{5\times7}+\frac{3}{7\times9}+....+\frac{3}{47\times49}\)

Answer 1

\(\Rightarrow\)C . \(\frac{2}{3}\) =\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\)....+\(\frac{2}{47.49}\)

\(\Rightarrow C.\frac{2}{3}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{47}-\frac{1}{49}\)

\(\Rightarrow C=\left(\frac{1}{3}-\frac{1}{49}\right)\div\frac{2}{3}\)

\(\Rightarrow C=\frac{46}{147}\div\frac{2}{3}\)

\(\Rightarrow C=\frac{23}{49}\)

Vậy C = \(\frac{23}{49}\)

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