The coefficient of x7
in the expression
(1 + x)10 + x(1 + x)9
+ x2(1 + x)8
+ ......+ x10 is:
Solution
(1 + x)<sup>10</sup> + x(1 + x)<sup>9</sup>
+ x<sup>2</sup>(1 + x)<sup>8</sup>
+ ......+ x<sup>10</sup>
<br><br>This is a G.P where
<br><br>First term, a = (1 + x)<sup>10</sup>
<br><br>common ratio, r = ${x \over {1 + x}}$
<br><br>Number of terms = 11
<br><br>Sum of G.P
<br><br>= $${{{{\left( {1 + x} \right)}^{10}}\left( {1 - {{\left( {{x \over {1 + x}}} \right)}^{11}}} \right)} \over {1 - {x \over {1 + x}}}}$$
<br><br>= (1 + x)<sup>11</sup>
– x<sup>11</sup>
<br><br>So Coefficient of x<sup>7</sup>
is <sup>11</sup>C<sub>7</sub> = 330
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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