Geometry EOC Practice
3. Find the measure of each labeled angle.
B(2x)
A (3x - 20°
C (2x - 15)

M M M

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Ответ:

lizzepacheco

05.05.2022

Mathematics

Factor out 1/n⁴, and distribute the sum over each term:

$\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac1{n^4}\sum_{i=1}^n(2i^3-3i)$

$\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac2{n^4}\sum_{i=1}^ni^3-\frac3{n^4}\sum_{i=1}^ni$

Recall the following formulas:

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

So we have

$\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac{n^2(n+1)^2}{2n^4}-\frac{3n(n+1)}{2n^4}=\boxed{\dfrac{(n+1)(n^2+n-3)}{2n^3}}$

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Geometry EOC Practice 3. Find the measure of each labeled angle. B(2x) A (3x - 20° C (2x - 15) M M M