\n" ); document.write( "(A) 1 + (1 + x) + (1 + x)^2 + ... + (1 + x)^20
\n" ); document.write( "(B) (1 + x)^2 + (1 + x)^3 + (1 + x)^4 + (1 + x)^5 + .... + (1 + x)^10
\n" ); document.write( "[Note: Here ^ means power]
Algebra.Com's Answer #814846 by greenestamps(13200)![\"\"](\"/images/stars/stars-13.gif\")  You can put this solution on YOUR website! \n" ); document.write( "The second one is trivial; only the expansion of the last term in the sum contains an x^10 term, and the coefficient of that term is clearly 1. \n" ); document.write( "(B) ANSWER: 1 \n" ); document.write( "In the first one, there is no x^10 term until we get to (1+x)^10. Then the coefficients of the x^10 terms in the expansion of the remaining terms in the given sum are... \n" ); document.write( "(1+x)^10: C(10,10) \n" ); document.write( "(1+x)^11: C(11,10) \n" ); document.write( "(1+x)^12: C(12,10) \n" ); document.write( "... \n" ); document.write( "(1+x)^20: C(20,10) \n" ); document.write( "The coefficient of the x^10 term in the sum is then found using the \"hockey stick\" equation for Pascal's Triangle: \n" ); document.write( "C(10,10)+C(11,10)+C(12,10)+...+C(20,10) = C(21,11) \n" ); document.write( "ANSWER: C(21,11) (which is the same as C(21,10)) \n" ); document.write( " \n" ); document.write( " |