Question 1029339
{{{sum((n(n+1)(2n+1)),n=9,49)= sum((2n^3+3n^2+n),n=9,49)}}}
{{{sum((n(n+1)(2n+1)),n=9,49)=2*sum(n^3,n=9,49)+3*sum(n^2,n=9,49)+sum(n,n=9,49)}}}
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{{{sum(n^3,n=1,k)=(1/4)k^2(k+1)^2}}}
{{{sum(n^2,n=1,k)=(1/6)k(k+1)(2k+1)}}}
{{{sum(n^2,n=1,k)=k(k+1)/2}}}
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{{{sum(n^3,n=1,8)+sum(n^3,n=9,49)=(1/4)49^2(49+1)^2}}}
{{{(1/4)8^2(8+1)^2+sum(n^3,n=9,49)=(1/4)49^2(50)^2}}}
{{{1296+sum(n^3,n=9,49)=1500625}}}
{{{sum(n^3,n=9,49)=1499329}}}
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{{{sum(n^2,n=1,8)+sum(n^2,n=9,49)=(1/6)49(50)(99)}}}
{{{(1/6)8(9)17+sum(n^2,n=9,49)=(1/6)49(50)(99)}}}
{{{204+sum(n^2,n=9,49)=40425}}}
{{{sum(n^2,n=9,49)=40221}}}
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{{{sum(n,n=1,8)+sum(n,n=9,49)=(1/2)49(50)}}}
{{{(1/2)8(9)+sum(n,n=9,49)=(1/6)49(50)(99)}}}
{{{36+sum(n,n=9,49)=1225}}}
{{{sum(n,n=9,49)=1189}}}
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So then putting it all together,
{{{sum((n(n+1)(2n+1)),n=9,49)=2*sum(n^3,n=9,49)+3*sum(n^2,n=9,49)+sum(n,n=9,49)}}}
{{{sum((n(n+1)(2n+1)),n=9,49)= 2*1499329+3*40221+1189}}}
{{{sum((n(n+1)(2n+1)),n=9,49)=3120510}}}