1.21+3.41+5.61+...+49.501
=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{49}-\frac{1}{50}=1−21+31−41+51−61+...+491−501
=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{49}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)=(1+31+51+...+491)−(21+41+61+...+501)
=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)=(1+21+31+...+501)−2(21+41+61+...+501)
=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{25}\right)=(1+21+31+...+501)−(1+21+31+...+251)
=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}=261+271+281+...+501
=> đpcm
