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Use the geometric sequence of numbers 1, 1/3, 1/9, 1/27… to find the following:

Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.
Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
What observation can make about the successive partial sums of this series? In particular, what number does it appear that the sum will always be smaller than?

These are standard formulas. I will be happy to critique your thinking.

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  1. S10 =a(r^n -1)/r-1
    S10=? r=⅓÷1=⅓ a=1 n=10

    By substitution,

    S10=1(⅓^10-1)/⅓-1
    S10 = -0.9999/-⅔
    S10= 1.49985...

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