document.write( "Question 252353: sum of the first 100 terms for the series:
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document.write( "(1*2*3)+(2*3*4)+(3*4*5)+..................... \n" );
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Algebra.Com's Answer #184213 by palanisamy(496)![]() ![]() ![]() You can put this solution on YOUR website! Lset S = (1*2*3)+(2*3*4)+(3*4*5)+.....................100 terms \n" ); document.write( "The nth term Tn = n*(n+1)*(n+2) \n" ); document.write( " = n*(n^2+2n+n+2) \n" ); document.write( " = n*(n^2+3n+2) \n" ); document.write( " = n^3+3n^2+2n \n" ); document.write( "Sum to n terms = sum( n^3 +3n^2+2n, i=1, n ) \n" ); document.write( " = n^2(n+1)^2 /4 + 3 n(n+1)(2n+1)/6 + 2n(n+1)/2 \n" ); document.write( "Put n = 100 \n" ); document.write( "Sum to 100 terms = (100)^2(101)^2 /4 +3x100x(101)x(201)/6 +100(101) \n" ); document.write( " = 25502500+1015050+10100 \n" ); document.write( " = 26527650 \n" ); document.write( " |