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navik [9.2K]
3 years ago
8

Does the following infinite series converge or diverge? Explain your answer. 1/2 - 2/9 + 4/27 - 8/81

Mathematics
1 answer:
Rina8888 [55]3 years ago
4 0
Something tells me the first term is supposed to be \dfrac13, not \dfrac12. In that case, the series would be

\displaystyle\sum_{n=0}^\infty\frac{(-2)^n}{3^{n+1}}=\frac13\sum_{n=0}^\infty\left(-\frac23\right)^n

which is geometric with a ratio less than 1, so the infinite series will converge, and moreover will converge to

\dfrac13\cdot\dfrac1{1+\frac23}=\dfrac15

Even if the first term was \dfrac12, the series will still converge, but we can't write it as we did above. Not counting the first term, we still have a convergent geometric series.
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$100

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Given:

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If the amount collected from sales on Wednesday was <u>$75 greater</u> than the amount collected from sales on Tuesday, then Tuesday's sales were $75 <u>less</u> than Wednesday's sales:

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If the amount collected from sales on Wednesday was <u>two times as great</u> as the amount collected from sales on Monday, then Monday's sales were <u>half</u> Wednesday's sales:

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