S = 2*4+4*6+6*8+...+46*48+48*50
S6 = 2*4*6+4*6*6+6*8*6+........................+46*48*6+48*50*6
S6=2*4*(6-0)+4*6*(8-2)+6*8*(10-4)+.................................+46*48*(50-44)+48*50*(52-46)
S6 = 2*4*6+4*6*8-2*4*6+6*8*10-4*6*8+..........................................+46*48*50-44*46*48+48*50*52-46*48*50
S6 = 48*50*52=124800
S=124800/6=20800
\(S=2\cdot4+4\cdot6+...+48\cdot50\)
\(S=2\left(1\cdot2+2\cdot3+...+24\cdot25\right)\)
\(\Rightarrow3S=2\left(1\cdot2\left(3-0\right)+2\cdot3\left(4-1\right)+...+24\cdot25\left(26-23\right)\right)\)
\(\Rightarrow3S=2\left(1\cdot2\cdot3-0\cdot1\cdot2+2\cdot3\cdot4-1\cdot2\cdot3+...+24\cdot25\cdot26-23\cdot24\cdot25\right)\)
\(\Rightarrow3S=2\cdot24\cdot25\cdot26\)
\(\Rightarrow S=2\cdot8\cdot25\cdot26=10400\)
\(\Rightarrow6S=10400\cdot6=62400\)
