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

Does the following infinite series converge or

Ответ:

yashajanjan8550

13.03.2022

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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Ответ:

nakeytrag

30.07.2020

Mathematics

No; he should have multiplied 800 by .95 and made sure that the total weight of the equipment was less than that amount. Hope this helps :)

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

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