0^2 - 1^2 + 2^2 - 3^2 + 4^2 - ..... - 99^2 + 100^2 = ?

• 0^2 - 1^2 + 2^2 - 3^2 + 4^2 - ..... - 99^2 + 100^2
  
  = (2^2-1^2)+(4^2-3^2)+(6^2-5^2)+...+(100^2-99^2)
  
  = 2+1 + 4+3 +6+5 +... + 100+99
  
  = 1+2+3+4+....+99+100
  
  = 100*(100+1)/2
  
  = 5050
• 10 years agoHelpfull: Yes(5) No(4)
• 0^2 - 1^2 + 2^2 - 3^2 + 4^2 - ..... - 99^2 + 100^2
  = (2^2-1^2)+(4^2-3^2)+(6^2-5^2)+...+(100^2-99^2)
  = 3+7+11+15+...195+199 total 50 terms
  = (50/2)*(3+199)= 25*202=5050
  
  
  
• 10 years agoHelpfull: Yes(2) No(3)
• (0^2+2^2+4^2+_ _ +100^2)-(1^2+3^2+5^2+_ _ +99^2)
  nth term of series (2n)^2-(2n-1)^2 [where n=50]
  4n^2-4n^2+4n-1=4n-1
  to take sum applying sigma or summation
  4sigma n-sigma 1 [sigma 1 to n times is n]
  4 sigma n-n
  (4*n(n+1)/2)-n [taking n=50]
  (4*50*51/2)-50=5050
  sum of series is 5050
  
  
• 10 years agoHelpfull: Yes(0) No(0)