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

Can someone please answer these 2 questions. The cross section of a sphere is shown. What is the area of the cross section ? This cylinder is 8 inches tall an
what did scientist observe when they studied the magnetic fields of rocks on the sides of mid ocean ridges?
determine if 9|x|+y=4 is a function
Solve the quadratic equation by completing the square. QUESTION ATTCHED BELOW!!!!!!!!!!PLEASES HELP!!REALLY LOST!!!!!!!
Which of the following statements best explains why producers conduct market research?
Question 8...................
Which word best completes the sentence? The record producer is____. A)he B)Him
Lisa was trying to park her car. She moved her car forward at a constant velocity for 5 seconds, and then backward at a constant velocity for 10 seconds. She th
Need help please ! ​
U is the set of positive integers less than 18. G is the set of positive factors of 12. What is the complement of set G in universe U.