The remainder when 10^10 +10^100 +10^1000 +.......+10^10000000000 is divided by 7 is
A)0
b)1
c)2
d)5

• 5
  10%7=3, (10^3)%7=6 => -1
  so,
  10^10=(10^3)^3 * 10 mod 7=(-1)*10=4
  10^100=(10^3)^33 *10 mod 7=(-1)*10=4
  10^1000=(10^3)^333 *10 mod 7=(-1)*10=4
  10^10000=(10^3)^3333 *10 mod 7=(-1)*10=4
  ....
  ....
  ....
  10^10000000000=(10^3)^3333333333 *10 mod 7=(-1)*10=4
  so,
  (4*10)%7=5
• 9 years agoHelpfull: Yes(0) No(4)