Question 1177007
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Your presentation of the problem is flawed; the information as given is nonsense.<br>
I don't know if you posted it incorrectly, or if it was incorrect when it was given to you.<br>
When the problem is presented correctly, the solution is simple.<br>
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Here is how the problem should have been posted:<br>
Find the sum in terms of n for<br>
{{{sum(3k^2-5k+7,1,n)}}}<br>
Given:<br>
{{{sum(k^2,1,n)=(n(n+1)(2n+1))/6 }}}  (The "k^2" was missing in your post, making the statement meaningless)<br>
and<br>
{{{sum(k,1,n)=(n(n+1))/2 }}}  (likewise, the "k" was missing)<br>
It should also be obvious that<br>
{{{sum(1,1,n)=n}}}<br>
Then...<br>
{{{sum(3k^2-5k+7,1,n)=3*sum(k^2,1,n)-5*sum(k,1,n)+7*sum(1,1,n)=3((n(n+1)(2n+1))/6)-5((n(n+1))/2)+7(n)}}}<br>
Then simplify if required.<br>