Question

 

2	+	2	+ … +	2	=
5 x 7		7 x 9		145 x 147

Answer 1

\(=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{145}-\dfrac{1}{147}\)

\(=\dfrac{1}{5}-\dfrac{1}{147}=\dfrac{142}{735}\)

Answer 2

\(\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{145.147}\)

\(=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{145}-\dfrac{1}{147}\)

\(=\dfrac{1}{5}-\dfrac{1}{147}\)

\(=\dfrac{147}{735}-\dfrac{5}{735}\)

\(=\dfrac{142}{735}\)

Answer 3

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