Given triangle ABC, which equation could be used to find the measure of <B?

Mathematics

1 answer:

jarptica [38.1K]2 years ago

4 0

Answer:

You would most likely would want to use Pythagorean Theorem, witch is, a²+b²=c²

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It's not clear what your series is, so I'm going to take a wild guess on what it is you mean:

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$=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n-1}}{(2n-1)!}\prod_{k=1}^n(2k-1)$

For the sum to be absolute convergent, the sum of the absolute value of the summand must converge, so you are really examining the convergence of

$\displaystyle\sum_{n=1}^\infty\frac1{(2n-1)!}\prod_{k=1}^n(2k-1)$

This is easily checked with the ratio test:

$\displaystyle\lim_{n\to\infty}\left|\frac{\displaystyle\dfrac1{(2(n+1)-1)!}\prod_{k=1}^{n+1}(2k-1)}{\displaystyle\dfrac1{(2n-1)!}\prod_{k=1}^n(2k-1)}\right|=\lim_{n\to\infty}\left|\frac{\dfrac{1\times3\times5\times\cdots\times(2n-1)\times(2n+1)}{(2n+1)!}}{\dfrac{1\times3\times5\times\cdots\times(2n-1)}{(2n-1)!}}\right|$
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Since $\sum|a_n|$ converges by the ratio test, the series $\sum a_n$ converges absolutely.