nannagarvey2501 nannagarvey2501

01-08-2017
Mathematics

contestada

Find the sum of the series. 1 + z/5 + z^2/25 + z^3.125

Respuesta :

LammettHash LammettHash

01-08-2017

[tex]1+\dfrac z5+\dfrac{z^2}{25}+\dfrac{z^3}{125}+\cdots=\displaystyle\sum_{k=0}^\infty\left(\frac z5\right)^k[/tex]
[tex]=\dfrac1{1-\frac z5}=\dfrac5{5-z}[/tex]

provided that [tex]\left|\dfrac z5\right|<1\iff|z|<5[/tex].

Answer Link

Otras preguntas

What is one advantage of outlining a speech before presenting it?

If s = 1/3 unit and A = 18s²,what is the value of A, in square units? ____ square unit(s). (Input whole number only.)

A deck of 52 cards is dealt out to 4 players. what is the probability that one of the players receive all 13 hearts

How to make an equation with numbers 0.25, 7.00, and 27

Helpppppppp pleaseeeeeeeeee

who launched the meiji restoration

Which missionary helped spread Christianity across the Roman empire?

what mountain range near the pacific coast still has active volcanoes?

For dimensioning of steel angles, the length of the longer leg is noted first. true false

when you see something, your brain processes the visual information so that you are aware of it. Most of this processing occurs in the ____ mind