Linda C. answered • 12/09/14
Tutor
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Engaging teacher fro Calculus, Precalculus, Trigonometry, and Algebra
Can you see the pattern? The signs are alternating, the numerator is just counting, and the denominator is of the form 3n. We could just continue the pattern for a few more terms, or recognize that each term can be represented by:
A(n)=(-1)n(n/3n)
That first part, with the -1 will just allow the terms to alternate in sign. Look at the second term of 2/9. If we plug 2 in for n, we get (-1)2(2/32), or 2/9, so it appears to work.
A(9)=(-1)9(9/39) = -9/19,683, which can be simplified to -1/2187, but I would probably leave it in the first form, to match the other terms.
