Question

PLZ ANSWER THANK YOU

Answer 1

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

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