Question
Using binomial theorem write down the expansions of the following:
(1 - 3x)7
Using binomial theorem write down the expansions of the following:
(1 - 3x)7
The expansion of (x + y)n has n + 1 terms so the expansion of (1 - 3x)7 has 8 term Using binomial theorem to expand, we get
$(1-3\text{x})^7={^7\text{C}}_0(1)^7(3\text{x})^0-{^7\text{C}}_1(3\text{x})+{^7\text{C}}_2(3\text{x})^2-{^7\text{C}}_3(3\text{x})^3\\+{^7\text{C}}_4(3\text{x})^4-{^7\text{C}}_5(3\text{x})^5-{^7\text{C}}_6(3\text{x})^6$
$=1-21\text{x}+21\times9\text{x}^2-35\times3^3\text{x}^3+35\times3^4\text{x}^4-\\21\times3^5\text{x}^5+7\times3^6\text{x}^6-3^7\text{x}^7$
$=1-21\text{x}+189\text{x}^2-945\text{x}^3+2835\text{x}^4-5103\text{x}^5+5103\text{x}^6-2187\text{x}^7$
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$\frac13,\frac19,\frac{1}{17}\ ...\text{is}\frac{1}{19683}?$