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 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

Based on what you know about Greek gods, why is Danaë proud that her son's father is Zeus?
What is the y-coordinate of the point of intersection for the two lines given below? A: 4 B: -14 C: -3 D: -2
Which molecules are used to produce glucose during the calvin cycle? A. ADP and NADP+B. ATP and NADPHC. Chlorophyll and Oxygen D. Carbon Dioxide and Water​
Thomas Paine wrote: the Articles of Confederation the Constitution Common Sense
Read the following passage. NASA is developing a first-ever robotic mission to visit a large near-Earth asteroid, collect a multi-ton boulder from its surface,
Complete the following analogy: sugar
5. Where is the epiglottis and what purpose does it serve? **​
The last answer choice is 15/2, 10 Helppp
Make the following sentence more active. The racing team was praised by the winning cyclist. (3 points) The winning cyclist praised the racing team. The cyclist
Why is a combination of diet and physical activity best for maintaining ideal levels of body fat?