jade3 wrote:
The remainder when 1+3+3^2+3^3+..........+3^200 is divided 13.
A.12
B.7
C.0
D.5
E.3
A.12
B.7
C.0
D.5
E.3
1+3+3^2+3^3+..........+3^(201-1) = (3^201 - 1)/(3-1) = (3^201 - 1) / 2
Now by 13 = (3^201 - 1) / 26 = (3^3)^67 - 1 / 26 = (26+1)^67 - 1 / 26 = (26)^67/26....... (1^67/26 - 1/26)
= An integer quotient and from the last part 0 . so remainder = 0