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The sum $1^2 + 2^2 + 3^2 + 4^2 + \ldots + n^2 = n(n+1)(2n+1) \div 6$. What is the value of $21^2 + 22^2 + \ldots + 40^2$?

 Jul 3, 2015

Best Answer 

 #5
avatar+583 
+13

Awesomeee's question is 21^2+22^2+...+40^2

not 1^2+2^2+3^2+4^2+....39^2+40^2

21^2+22^2+...+40^2=[(1^2+2^2+3^2+...39^2+40^2)-(1^2+2^2+...19^2+20^2)]/6

                                =$${\frac{\left[{\mathtt{40}}{\mathtt{\,\times\,}}\left({\mathtt{40}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right){\mathtt{\,\times\,}}\left({\mathtt{81}}\right){\mathtt{\,-\,}}{\mathtt{20}}{\mathtt{\,\times\,}}\left({\mathtt{20}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right){\mathtt{\,\times\,}}{\mathtt{41}}\right]}{{\mathtt{6}}}} = {\mathtt{19\,720}}$$

 Jul 4, 2015
 #5
avatar+583 
+13
Best Answer

Awesomeee's question is 21^2+22^2+...+40^2

not 1^2+2^2+3^2+4^2+....39^2+40^2

21^2+22^2+...+40^2=[(1^2+2^2+3^2+...39^2+40^2)-(1^2+2^2+...19^2+20^2)]/6

                                =$${\frac{\left[{\mathtt{40}}{\mathtt{\,\times\,}}\left({\mathtt{40}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right){\mathtt{\,\times\,}}\left({\mathtt{81}}\right){\mathtt{\,-\,}}{\mathtt{20}}{\mathtt{\,\times\,}}\left({\mathtt{20}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right){\mathtt{\,\times\,}}{\mathtt{41}}\right]}{{\mathtt{6}}}} = {\mathtt{19\,720}}$$

fiora Jul 4, 2015
 #6
avatar+128577 
0

Thanks, fiora....I totally mis-read that one.....!!!!

 

 

 

 Jul 4, 2015

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