The coefficient of x 53 in the expansion of - m -0100100 C m x -3100- m 2 m isA- 100 C47B- 100 C 53C- -100 C53D- -100 C100

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Ratio and Proportion

The coefficie...

Question

The coefficient of $x^{53}$ in the expansion of $100 \sum m = 0$ $^{100} C_{m}$ $(x - 3)^{100 - m} 2^{m}$ is

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x^{53}

100 \sum m = 0^{100} C_{m} (x - 3)^{100 - m} 2^{m}

x^{53}

\sum_{m = 0}^{100} {C_{m}}^{100} {(x - 3)}^{100 - m} 2^{m}

The coefficient of $x^{53}$ in $\sum_{r = 0}^{100}^{100} C_{r} (x - 3)^{100 - r} 2^{r}$ is

x^{53}

\sum_{m = 0}^{100} {^{100} C}_{m} {(x - 3)}^{100 - m} . 2^{m}

x^{53}

100 \sum m = 0^{100} C_{m} (x - 3)^{100 - m} \cdot 2^{m}

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