Question

Tính A = \(\frac{1}{5x7}\)+ \(\frac{1}{7x9}\)+ \(\frac{1}{9x11}\)+...+ \(\frac{1}{2011x2013}\)

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Answer 1

\(.A=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2011}-\frac{1}{2013}\right)\)

\(A=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{2013}\right)\)

\(A=\frac{1004}{10065}\)

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Answer 2

A=1/5x7+11/7x9+1/9x11+....+1/2011x2013

2xA=2x(1/5x7+1/7x9+1/9x11+...+1/2011x2013

2xA=2/5x7+2/7x9+2/9x11+...+2/2011x2013

2xA=1/5-1/7+1/7-1/9+1/9-1/11+...+1/2011-1/2013

2xA=1/5-1/2013

2xA=2013/10045-5/10045

2xA=2008/10045

A=2008/10045:2

A=2008/10045x1/2

A=1004/10045