You can first condense the series to make it simpler to study. If <em>n</em> is odd, then <em>n</em> = 2<em>k</em> - 1, and if <em>n</em> is even, then <em>n</em> = 2<em>k</em> for some <em>k</em> ≥ 1. So for each <em>k</em>, you can pair up the <em>k</em>-th terms of the odd- and even-indexed series.
odd:
![\dfrac1{3^{\frac{n+3}2}}=\dfrac1{3^{k+1}}](https://tex.z-dn.net/?f=%5Cdfrac1%7B3%5E%7B%5Cfrac%7Bn%2B3%7D2%7D%7D%3D%5Cdfrac1%7B3%5E%7Bk%2B1%7D%7D)
even:
![\dfrac1{3^{\frac n2}}=\dfrac1{3^k}](https://tex.z-dn.net/?f=%5Cdfrac1%7B3%5E%7B%5Cfrac%20n2%7D%7D%3D%5Cdfrac1%7B3%5Ek%7D)
So the series can be re-indexed as
![\displaystyle\sum_{n=1}^\infty a_n=\sum_{k=1}^\infty a_k=\sum_{k=1}^\infty \left(\frac1{3^{k+1}}+\frac1{3^k}\right)=\sum_{k=1}^\infty\frac4{3^{k+1}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5E%5Cinfty%20a_n%3D%5Csum_%7Bk%3D1%7D%5E%5Cinfty%20a_k%3D%5Csum_%7Bk%3D1%7D%5E%5Cinfty%20%5Cleft%28%5Cfrac1%7B3%5E%7Bk%2B1%7D%7D%2B%5Cfrac1%7B3%5Ek%7D%5Cright%29%3D%5Csum_%7Bk%3D1%7D%5E%5Cinfty%5Cfrac4%7B3%5E%7Bk%2B1%7D%7D)
By the root test, the series converges, since
![\displaystyle\lim_{k\to\infty}\sqrt[k]{\left|\frac4{3^{k+1}}\right|}=\frac13\lim_{k\to\infty}\left(\frac43\right)^{\frac1k}=\frac13](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bk%5Cto%5Cinfty%7D%5Csqrt%5Bk%5D%7B%5Cleft%7C%5Cfrac4%7B3%5E%7Bk%2B1%7D%7D%5Cright%7C%7D%3D%5Cfrac13%5Clim_%7Bk%5Cto%5Cinfty%7D%5Cleft%28%5Cfrac43%5Cright%29%5E%7B%5Cfrac1k%7D%3D%5Cfrac13%3C1)
Answer:
105.98
Step-by-step explanation:
to find area you have to do pi x radius which is half the diameter, in this case the radius is 1.5 so u would plug that in which gives you 7.068583471. then you would multiply that by 15 to get the total area of ALL the latkes.
<h2>
![{\blue {\boxed {\colorbox {black} {\blue {King\:Brainly01}}}}}](https://tex.z-dn.net/?f=%7B%5Cblue%20%7B%5Cboxed%20%7B%5Ccolorbox%20%7Bblack%7D%20%7B%5Cblue%20%7BKing%5C%3ABrainly01%7D%7D%7D%7D%7D)
</h2>
![\:](https://tex.z-dn.net/?f=%5C%3A)
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A × B + C - C - A
1 × 4 + 3 - 3 - 1
4 + 3 - 3 - 1
7 - 3 - 1
4 - 1
3
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Answer:
2884
Step-by-step explanation:
First plug in -10 for x, which would look like this: 734 + (-215 * (-10) ) =
Then, first you calculate everything in the parenthesis, which is (-215) * (-10)
and the equation would look like this after you multiply: 734 + 2150 =
If you noticed the number turned out positive after we multiplied, that is because - number times a - number would always be positive, just like if you divide - number by a - number your answer would be positive.
Your last step would be adding 734 with 2150. : 734 + 2150 = 2884
+ 734
2150
_____
2884
And the answer would be 2884
A) angle A = 180-135= 45 degrees
Angles A and 135 are supplementary angles
b) angle B= 135 degrees
because the two 135 angles are vertical angles ( opposite angles made by two intersecting line)
c) angle C = 45 degrees
because angles C and angles A are corresponding angles since line (1) and line (2) are parallel