Question 1184312
(A)  {{{1 + (1 + x) + (1 + x)^2 + "..." + (1 + x)^20  = ((1 + (1 + x) + (1 + x)^2 + "..." + (1 + x)^20 )((1+x) - 1))/((1+x) - 1) = ((1+x)^21-1)/x}}}


={{{ (sum((matrix(2,1,21,k))*x^(21-k), k=0,21) - 1)/x}}}


={{{(x^21 + 21x^20 + "..." + (matrix(2,1,21,9))*x^12 + (matrix(2,1,21,10))*x^11 + (matrix(2,1,21,11))*x^10 + "..." +21x)/x


 =  x^20 + 21x^19 + "..." + (matrix(2,1,21,9))*x^11 + highlight((matrix(2,1,21,10)))*x^10 + (matrix(2,1,21,11))*x^9 + "..." +21
 }}}


(B) This should be more manageable than (A).  Note that the term {{{x^10}}} appears in the last term of the expression only, which is {{{(1+x)^10}}}.  

Therefore the coefficient of {{{x^10}}} is {{{highlight(1)}}}