Difference between sum of square of 2 digit odd number to sum of square of 2 digit even no.(11^2+13^2....-12^2+14^2....)

• ( 11^2 + 13^2 + .....+ 99^2 ) - ( 10^2 + 12^2 + .........+ 98^2 )
  
  = (11^2 - 10^2) + (13^2 - 12^2) + ............+ (99^2 - 98^2).
  
  = (11 + 10) + (13+12) +.........+(99+98)
  
  = (10+11+12+13+......+98+99)
  
  = (1+2+....+9+10+11+12+13+......+98+99) -(1+2+3+....+9)
  
  = 99*100/2 - 9*10/2
  
  = 4905
• 9 years agoHelpfull: Yes(53) No(1)
• (11^2 + 13^2 + .....+ 99^2) - (10^2 + 12^2 + .........+ 98^2)
  We can write this expr.
  (11^2 - 10^2) + (13^2 - 12^2) + ............+ (99^2 - 98^2).
  Again, we can split
  (11 + 10)(11-10) +(13+12)(13-12) +.........(99+98)(99-98)
  21 + 25 + 29 +.......197.
  in a.p form
  s=n(a+l)/2
  s=45(21+197)/2
  s=4905
• 9 years agoHelpfull: Yes(10) No(0)
• 12^2-11^2=23
  14^2-13^2=27
  .
  .
  .
  98^2-97^2=195
  We get an AP as 23, 27, 31..........,195 with difference of 4
  Adding this we get 4796
  99^2-4796= 5005
  
• 9 years agoHelpfull: Yes(4) No(6)
• (11^2 + 13^2 + .....+ 99^2) - (10^2 + 12^2 + .........+ 98^2)
  we can write this expr.
  (11^2 - 10^2) + (13^2 - 12^2) + ............+ (99^2 - 98^2).
  again we can split
  (11 + 10)(11-10) +(13+12)(13-12) +.........(99+98)(99-98)
  21 + 25 + 29 +.......197.
  in a.p form
  ans== 4708
• 9 years agoHelpfull: Yes(2) No(3)
• (12^2+14^2+......+98^2) - (11^2+13^2+......99^2)
  12.2^(45-1) - (11.2^(44-1)) =2^43*23 ANS.
• 9 years agoHelpfull: Yes(0) No(9)
• thnx @RAKESH :)
• 9 years agoHelpfull: Yes(0) No(0)