What is the unit digit of 1 +9 +9^2 + 9^3 + .... 9^2773 ?

• 9^0=1
  9^1=9
  9^2=81 unit digit is 1
  9^3=729 unit digit is 9
  hence for odd powers unit digit is 9 and for even powers unit digit is 1
  From 0 to 2773 number of terms= 2774
  2774/2= 1387
  so 1387 odd and 1387 even numbers.
  
  so (1387*1)+(1387*9)= 1387+12483
  here the unit digit is 7+3=10
  hence the answer is 0
  
  
• 8 years agoHelpfull: Yes(55) No(2)
• 0
  9^odd=unit digit is 9
  9^even =unit digit is 1
  1+9+1+9+1..............9=0
• 8 years agoHelpfull: Yes(17) No(4)
• 1 + 9 + 1 + 9 ... ....1 + 9 + 1
  1+9 = 10 unit place is zero this happens till 2772
  at 2773 the units place is 1
• 8 years agoHelpfull: Yes(8) No(5)
• 1. 1
  2.9
  3.1
  4.9
  5.1
  6.9
  n.9 Ans : 0
• 8 years agoHelpfull: Yes(4) No(0)
• Answer is 0.
  9^1=9
  9^2=81
  9^3=729
  9^4=6561, By this we can say that,9 has only two cycles,(look at the unit digit,it changes from 9-1 &again 9-1).If the power of NINE is EVEN,then the unit digit will be 1, If the power of NINE is ODD,then the unit digit will be 9. Now add these 9+1=10, therefore the unit digit is 0.
• 7 years agoHelpfull: Yes(4) No(0)
• i would be saying 1 beacuse
  9+9^2 so unit difit is 0
  similarly
  9^2772+9^2773
  unnit digit is 1
  
  now if u add 1 in the first
  unit digit is 1
• 8 years agoHelpfull: Yes(3) No(7)
• 9
  9^1=9 9^2=81 unit digit is 1
  9^3=729 unit digit is 9
  hence for odd powers unit digit is 9 and for even powers unit digit is 1
  so the unit digit of 9^2773=9
• 9 years agoHelpfull: Yes(2) No(6)
• Ans is 0 ..... 1 + 10 + 10 + 10 .... ( 1386) times + 9 = again 10 which is 0
  
• 8 years agoHelpfull: Yes(1) No(1)
• 9^1=9
  9^2=81 (units place is 1)
  9^3=729 (unit's place is 9)
  
  so alternatively 1 , 9 only coming . If power is odd number then unit's place is 9 . If power is even number then unit's place is 1 . so 2773 is and odd power therefore it ends with 9 as the units place
  
  1+9+1+9+...+1+9= ------0
  
  1+9=10 then the units place is 0
  
  Thus the Unit digit of the given qn is 0 (ZERO).
• 6 years agoHelpfull: Yes(1) No(0)
• 9 is a answer.because we take 9^2773. in this 2773 is a odd number .so unit degit is 9.
• 6 years agoHelpfull: Yes(1) No(1)
• 2773%4=1
  9^1=9
  so the unit digit is 9
  
• 8 years agoHelpfull: Yes(0) No(4)
• 1=1
  9=9
  9^2=81=1
  9^3=729=9
  9^2773=9
  1+9+1+9+9=9
• 8 years agoHelpfull: Yes(0) No(4)
• based on the power cycle of 9 we found that the unit digit of the above is 9.
• 7 years agoHelpfull: Yes(0) No(4)
• The power of odd 9 is 9 in the power cycle..
  hence the unit digit of 9+9^2+9^3+...+9^2773 is 9..
  and 9+1=10...hence the unit digit is 0.
• 7 years agoHelpfull: Yes(0) No(0)
• It is 1 for even powers and 9 for even.
  so, 1+9+1+9+.......1+9
  ans: 0
• 7 years agoHelpfull: Yes(0) No(0)
• 9^0 +9^1+9^2+......9^2773
  i.e 1+9+1+9+1+9.....
  making pair of 10
  hence unit digit is 0.
• 7 years agoHelpfull: Yes(0) No(0)
• 9. since last digit of the power is 3....for 9^3,the unit digit is 9
• 7 years agoHelpfull: Yes(0) No(0)
• 1+9^[1+1+1+...........+up to 2773]
  [1+1+1+...........+up to 2773]---------------> (2773*2774)/2----->1 (unit place)
  1+9^1= 1+9=10
  Ans: 0
• 6 years agoHelpfull: Yes(0) No(1)