<PRE><B>Question 1184312</B>
&lt;br&gt;
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.&lt;br&gt;
(B) ANSWER: 1&lt;br&gt;
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...&lt;br&gt;
(1+x)^10: C(10,10)
(1+x)^11: C(11,10)
(1+x)^12: C(12,10)
...
(1+x)^20: C(20,10)&lt;br&gt;
The coefficient of the x^10 term in the sum is then found using the &quot;hockey stick&quot; equation for Pascal&#39;s Triangle:&lt;br&gt;
C(10,10)+C(11,10)+C(12,10)+...+C(20,10) = C(21,11)&lt;br&gt;
ANSWER: C(21,11) (which is the same as C(21,10))&lt;br&gt;
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