Mathematics, 18.07.2019 13:00 Adithya27

75 points for the best ! , show all your work. does this series converge or diverge? and if it converges what is the sum? ∞ ∑ -4(-1/2)^n-1 n=1

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Answer from: 1162

Answers: the sum is convergentthe sum is -8/3======i assume this is what it looks like $\displaystyle\sum_{n=1}^{\infty} -4(-1/2)^{n-1}$ for a geometric series, when the common ratio r satisfies |r| < 1, the series is convergent. the geometric series converges because the absolute value of the common ratio (|-1/2| = 1/2) is less than 1.the sum for an infinite geometric series is given by s = a / (1 - r)where a is the first term and r is the common ratio.the first term is -4 since when we use the lower bound of summation (n=1) into the summand -4(-1/2)^(n-1), we get -4 as the first term.the sum is s = -4 / ( 1 - (-1/2) ) = -4/( 2/2+1/2 ) = -8/3 $s = \dfrac{-4}{1 - \left(- \frac{1}{2}\right)} = \dfrac{-4}{\frac{2}{2}+ \frac{1}{2}} = -\dfrac{8}{3}$ the sum is -8/3.

Answer from: Quest

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf =

pf = 6,25 u

ver más en -

step-by-step explanation:

Answer from: Quest

vwhat effect does the word head have on the meaning of this passage?

a. it demonstrates how intelligent he was.

b. it shows he was a favorite of the teachers.

c. it indicates he would be a good preacher.

d. it reveals how self-important he was.

how does the choice of the word head contribute to the passage’s tone?

a. it offers a sense of entitlement.

step-by-step explanation:

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75 points for the best ! , show all your work. does this series converge or diverge? and if it con...