4^2 + 2* 5^2 + 3* 6^2 +4* 7^2+...........+27*30^2 ?

• ∑ r^2 = n(n+1)(2n+1)/6
  ∑ r^3 = [n(n+1)/2]
  ∴ 4^2+(5^3+6^3+......30^3)-3(5^2+6^2+.....30^2)
  =16+(216225-100)-3*(9455-30) =187866
• 9 years agoHelpfull: Yes(8) No(5)
• 4^2+(5-3)*5^2+(6-3)*6^2+....(30-3)*30^2
  
  now the above eq become
  4^2+(5^3+6^3+......30^3)-3(5^2+6^2+.....30^2)
  apply formula and calculate.. :)
  
• 9 years agoHelpfull: Yes(6) No(3)
• ∑ r^3 = n2(n+1)2/4
  = (n(n+1)/2)2
  
  = n2(n+1)2
  ∴ ∑ r^2 = n(n+1)/2
  
  so=>
  16+(216225-100)-3*(9455-30) = 187866
  
• 9 years agoHelpfull: Yes(3) No(1)
• plz clearly explain how to solve this question..
• 8 years agoHelpfull: Yes(3) No(4)