Answer:
1, x/3, x^2/9, x^3/27, x^4/81
x^4 +3x^3+9x^2+27x+81
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81
Step-by-step explanation:
(x/3) ^i
i=0 (x/3)^0 = 1
i=1 (x/3)^1 = x/3
i=2 (x/3)^2 = x^2/3^2 = x^2/9
i=3 (x/3)^3 = x^3/3^3 =x^3/27
i=4 (x/3)^4 = x^4/3^4 =x^4/81
The sum is
1+(x/3) + x^2/9 + x^3/27 + x^4/81
We need a common denominator of 81
1*81/81 + x/3 *27/27 + x^2/9 *9/9 + x^3/27 *3/3 + x^4/81
81+27x + 9x^2 + 3x^3 +x^4
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81
Rewriting from largest power to smallest power
x^4 +3x^3+9x^2+27x+81
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81
