Question

0%2B%209%28%20%5Cfrac%7B%20%5Ccos%5E%7B2%7D%5Cinfty%20%7D%7B%20%7B%20%5Csin%7D%5E%7B2%7D%20%5Cinfty%20%7D%20%29%7D%7D" id="TexFormula1" title=" \large{\bold \red{ \sum \limits_{8}^{4} {x}^{2} + 9( \frac{ \cos^{2}\infty }{ { \sin}^{2} \infty } )}}" alt=" \large{\bold \red{ \sum \limits_{8}^{4} {x}^{2} + 9( \frac{ \cos^{2}\infty }{ { \sin}^{2} \infty } )}}" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

No solution

Step-by-step explanation:

We have

$\sum_{x=8}^{4}x^2 + 9\left(\dfrac{\cos^2(\infty)}{\sin^2(\infty)} \right)$

For the sum it is not correct to assume

$\sum_{x=8}^{4}x^2= 8^2 + 7^2+6^2+5^2+4^2 = 64+49+36+25+16 = 190$

Note that for

$\sum_{x=a}^b f(x)$

it is assumed $a\leq x \leq b$ and in your case $\nexists x\in\mathbb{Z}: a\leq x\leq b$ for $a>b$

In fact, considering a set $S$ we have

$\sum_{x=a}^b (S \cup \varnothing) = \sum_{x=a}^b S + \sum_{x=a}^b \varnothing$ that satisfy $S = S \cup \varnothing$

This means that, by definition $\sum_{x=a}^b \varnothing = 0$

Therefore,

$\sum_{x=8}^{4}x^2 = 0$

because the sum is empty.

For

$9\left(\dfrac{\cos^2(\infty)}{\sin^2(\infty)} \right)$

we have other problems. Actually, this case is really bad.

Note that $\cos^2(\infty)$ has no value. In fact, if we consider for the case

$\lim_{x \to \infty} \cos^2(x)$, the cosine function oscillates between $[-1, 1]$ , and therefore it is undefined. Thus, we cannot evaluate

$9\left(\dfrac{\cos^2(\infty)}{\sin^2(\infty)} \right)$

and then

$\sum_{x=8}^{4}x^2 + 9\left(\dfrac{\cos^2(\infty)}{\sin^2(\infty)} \right)$

has no solution