2 years ago

2/5 meters converted to centimeters

Mathematics

1 answer:

juin [17]2 years ago

8 0

The answer in centimetres is 250cm

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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B-4%7D%20%7D%7B%283%2B1%29-%282%2B3i%29%7D%20" id="TexFormula1" title

frozen [14]

$\sqrt{-4}$ can also be written as 2i
where i = √-1

$\frac{2i}{4-2-3i} = \frac{2i}{2-3i}$

Rationalizing denominator,

$\frac{2i(2+3i)}{(2-3i)(2+3i)} = \frac{4i-6}{4+9} = \frac{4i-6}{13}$

8 0

3 years ago

Show that a sequence {sn} coverages to a limit L if and only if the sequence {sn-L} coverages to zero.

Andreyy89

Let ${s_n}_{n\in\Bbb N}$ be a sequence that converges to $L$ . This means for any $\varepsilon>0$ , there is some $N$ such that $|s_n-L|$ for all $n>N$ . From this inequality we see that $|(s_n-L)-0|$ , so it follows that $s_n-L\to0$ .

On the other hand, let ${s_n-L}$ be a sequence that converges to 0. This means $|(s_n-L)-0|$ for all large enough $n$ , and we get the simpler inequality for free, $|s_n-L|$ , so it follows that $s_n\to L$ .