Найти более удобным способом 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+........+1/49*50

Question

Найти более удобным способом 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+........+1/49*50

Answer 1

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+........+1/49*50=

(2-1)/1*2+(3-2)/2*3+(4-3)/3*4+(5-4)/4*5+(6-5)/5*6+........+(50-49)/49*50=

=1/1-1/2+1/2-1/3+1/3-1/4+...+1/49-1/50=1-1/50=49/50=0.98