Using Maclaurin series, determine to exactly what value the following series converges: sum_{n=0}^inftyfrac{(ln5)^n}{n!}

CheemnCatelvew 2021-01-04 Answered
Using Maclaurin series, determine to exactly what value the following series converges:
n=0(ln5)nn!
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Obiajulu
Answered 2021-01-05 Author has 98 answers
Maclaurin Series expansion of ex
Let f(x)=ex
f(x)=f(0)+f(0)x1!+f(x)x22!+f(x)x33!+...
f(0)=e0=1
f(0)=e0=1
f(0)=e0=1
f(0)=e0=1... ans so on
Hence,
ex=1+x1+x22!+x33!+...
ex=n=0xnn!
Now we have given series n=0(ln5)nn!
If we compare it equation, we got here x=ln5
n=0(ln5)nn!=eln5
=5
Hence n=0(ln5)nn!=5
So , this series converges to 5

We have step-by-step solutions for your answer!

Jeffrey Jordon
Answered 2021-12-27 Author has 2495 answers

Answer is given below (on video)

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions