Question

Tính tổng S : (1+\(\dfrac{1}{1.3}\) ).(1+\(\dfrac{1}{2.4}\)).(1+\(\dfrac{1}{3.5}\))...(1+\(\dfrac{1}{2009.2011}\))

Answer 1

\(\left(1+\dfrac{1}{1.3}\right).\left(1+\dfrac{1}{2.4}\right).\left(1+\dfrac{1}{3.5}\right)......\left(1+\dfrac{1}{2009.2011}\right)\)

\(=\dfrac{4}{1.3}.\dfrac{9}{2.4}.\dfrac{16}{3.5}........\dfrac{4040100}{2009.2011}\)

\(=\dfrac{2.2.3.3.4.4.....................2010.2010}{1.3.2.4.3.5.................2008.2010.2009.2011}\)

\(=\dfrac{2.2010}{2011}\)

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