wht will be the remainder when expression 2^2+22^2+222^2+2222^2+....+22222...48times^2 divided by 9.

• 5
  2^2 % 9 = 4
  22^2 % 9 = 4^2 = 16 %9 = 7
  222^2 % 9 = 6^6 = 36 % 9 = 0
  now again 2222^2 % 9 = 4 and so 16 triplet of (4 , 7 , 0)= 11*16 = 176 % 9= 5
  
• 11 years agoHelpfull: Yes(34) No(12)
• (2^2 + 22^2 + 222^2...(2222...48times)^2) % 9
  
  [(4*(1^2) + 4(11^2) + 4(111^2)...] %9
  
  4[1^2 + 11^ 2 + 111^ 2...] % 9
  
  4[1 + (9+2)^2 + (108+3)^2...] % 9...(all terms of form (a+b)^2, where a is a multiple of 9, like 9, 108, 1107...)
  
  4[1^2 + 2^2 + 3^2+...+48^2} % 9 .........(since all terms of form a^2+2ab are divisible by 9)
  
  [4*48*49*97/6] % 9
  
  remainder = 5...
• 11 years agoHelpfull: Yes(27) No(7)
• 2^2 %9 =4
  22^2 %9 =7
  222^2 %9 =0
  2222^2 %9 =1
  
  22222^2 %9 =1
  222222^2 %9 =0
  2222222^2 %9 =4
  22222222^2 %9 =7
  
  So the same result is repeated so the combination 4 7 0 1 is repeated for 12 times
  so the resultant is 12*12 = 144
  final reminder is 144 % 9 =0
  
  Final answer is : ZERO
• 11 years agoHelpfull: Yes(23) No(1)
• Look the first four term
  (2^2)=4/9=4
  (22^2) / 9=7
  (222^2) / 9=0
  (2222^2) / 9=1
  
  now move for next four term
  (22222^2) / 9=1
  (222222^2) / 9=0
  (2222222^2) / 9=4
  (22222222^2) / 9=7
  
  Here we can observe that remainder in the first four term is same as
  the remainder in the next four term.
  and the process will continue for every next consecutive four terms
  
  Hence every remainder will occur four times.
  So
  (0*12+1*12+4*12+7*12) / 9
  (0+12+48+84) / 9
  144 / 9 (144 is divisible by 9)
  0
  
  Thus ANSWER is=0(ZERO).
• 10 years agoHelpfull: Yes(8) No(1)
• what is the correct answer...can anyone tell me plzzzzz
• 11 years agoHelpfull: Yes(1) No(0)
• ANS=2
  222^2=remainder 2
  2222^2=remainder 3
  22222^2=remainder 4
  222222^2=remainder 2
  2222222^2=remainder 3
  22222222^2=remainder 4
  222222222^2=remainder 3
  
  so 2.....^2=remainder=2
  
• 11 years agoHelpfull: Yes(0) No(18)
• 2^2(1^2+11^2+111^2+1111^2+11111^2+---------+111111......48times^2)%9
  =2^2(1^2+2^2+3^2+-----------+48^2)%9
  =(4*48*49*99)%(6*9)
  =2
  thats means answer is 2....
  
  
• 11 years agoHelpfull: Yes(0) No(2)
• 152096mod9=5
• 10 years agoHelpfull: Yes(0) No(2)
• 2^2 % 9 = 4
  22^2 % 9 = 7
  222^2 % 9 = 0
  2222^2%9=1
  now again 22222^2 % 9 = 4 and so 12 set of (4 , 7 , 0,1)= 12*12 = 144 % 9= 0.
• 8 years agoHelpfull: Yes(0) No(0)