Объяснение:
1/k!-(k²+k)/(k+2)!=1/k!-(k*(k+1)/(k!*(k+1)*(k+2))=((k+1)*(k+2)-k*(k+1))/(k+2)!=
=(k+1)*(k+2-k)/(k+2)!=2*(k+1)/(k+2)!=2*(k+1)/(k!*(k+1)*(k+2))=2/(k!*(k+2).
Объяснение:
1/k!-(k²+k)/(k+2)!=1/k!-(k*(k+1)/(k!*(k+1)*(k+2))=((k+1)*(k+2)-k*(k+1))/(k+2)!=
=(k+1)*(k+2-k)/(k+2)!=2*(k+1)/(k+2)!=2*(k+1)/(k!*(k+1)*(k+2))=2/(k!*(k+2).