Question

10 +12 + 14 + .... + 198 + 200

1/5*7+1/7*9+1/2011*2013

Answer 1

\(10+12+14+...+198+200\) có  \(\left(200-10\right):2+1=96\)( số hạng )

\(10+12+14+...+198+200\)\(=\left(200+10\right)\times96:2=10080\)

\(\frac{1}{5\times7}+\frac{1}{7\times9}+...+\frac{1}{1011\times2013}\)

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

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

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

\(=\frac{1}{2}\times\frac{2008}{10065}\)

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