Mathematics: Pllz me end of the year alot of stuff it do plz asap

Pllz me end of the year alot of stuff it do plz

Ответ:

tyneshiajones124

20.06.2020

Mathematics

The first question would be B) the second question is D) and the third question is A)

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Ответ:

querline87

03.01.2021

Mathematics

$\dfrac14+\dfrac2{4^2}+\dfrac1{4^3}+\dfrac2{4^4}+\cdots$
$=\left(\dfrac14+\dfrac1{4^2}+\dfrac1{4^3}+\dfrac1{4^4}+\cdots\right)+\left(\dfrac1{4^2}+\dfrac1{4^4}+\cdots\right)$
$=\displaystyle\sum_{n=1}^\infty\left(\frac14\right)^n+\sum_{n=1}^\infty\left(\frac14\right)^{2n}$
$=\displaystyle\sum_{n=0}^\infty\left(\frac14\right)^n-1+\sum_{n=0}^\infty\left(\frac14\right)^{2n}-1$
$=\displaystyle\sum_{n=0}^\infty\left(\frac14\right)^n+\sum_{n=0}^\infty\left(\frac1{16}\right)^n-2$
$=\dfrac1{1-\frac14}+\dfrac1{1-\frac1{16}}-2$
$=\dfrac25$

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Pllz me end of the year alot of stuff it do plz asap

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