Question

calculati:(a-b)^1+(a-b)^2+(a-b)^3+...+(a-b)^1995

Answer 1

notăm (a-b) = n
S = n+n² +n³ +........+n^1995 
nS = n² + n³ +..........+n^1996        nS - S = (n-1)S = n^1996 - n ⇒
⇒  S = n(n^1995 - 1)/(n-1)
S = (a-b)[(a-b)^1995 - 1)] / (a-b-1)