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7.Binomial Theorem
normal
Let ${\left( {1 + x + {x^2}} \right)^{20}}\left( {2x + 1} \right) = {a_0} + {a_1}{x^1} + {a_2}{x^2} + ... + {a_{41}}{x^{41}}$ , then $\frac{{{a_0}}}{1} + \frac{{{a_1}}}{2} + .... + \frac{{{a_{41}}}}{{42}}$ is equal to
A
$\left( {\frac{{{2^{21}} - 1}}{{21}}} \right)$
B
$\left( {\frac{{{3^{21}} - 1}}{{21}}} \right)$
C
$\left( {\frac{{{2^{20}} - 1}}{{20}}} \right)$
D
$\left( {\frac{{{3^{20}} - 1}}{{20}}} \right)$
Solution
$\int\limits_0^1 {{{\left( {1 + x + {x^2}} \right)}^{20}}} (2x + 1)dx$
$=\frac{a_{0}}{1}+\frac{a_{1}}{2}+\ldots .+\frac{a_{41}}{42}$
Standard 11
Mathematics
