posted by .

I need help understanding how the series of e derives into the exponential series using the binomial theorem.

Here is a link to a pic of a page in my book, regarding the exponential series:

ht tp://i46.tiny pic(.)(com)/qz0oat . jpg
(remove parentheses and spaces)
A couple of questions:

Where does the [1 + (1/k)]^k come from and why is it used?

Could you clarify the expansion of [1+(1/k)]^k?
I don't understand how it gets to ... k(1/k) + k(k-1)/2! (1/k^2) + ...

How does it end up with a 1 + 1 + 1[1-(1/k)]/2! + ...

Why are you finding the limit of the series?

And finally how do you end up with exponential series

x^n /n! = 1 + x + x^2/2! + ... ?

I'm confused and just really don't understand why or how you end up with everything. Help is VERY appreciated.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Using the index of a series as the domain and the value of the series as the range, is a series a function?
  2. Algebra

    Using the index of a series as the domain and the value of the series as the range, is a series a function?
  3. College Calculus (Binomial Series)

    Expand f(x) = (x+x^2)/((1-x)^3) as a power series and use it to find the sum of series (SUM from n=1 to infinity) (n^2)/(2^n) PLEASE HELP.
  4. calculus

    Where did the exponential series come from?
  5. calculus

    With power series, is an endpoint convergent if you plug it back into the original series, and get an alternating series that is conditionally convergent?
  6. calculus

    Consider ∞ ∑ [(3k+5)/(k²-2k)]ᵖ, for each p ∈ ℝ. k=3 Show this series { converges if p > 1 { diverges if p ≤ 1 Hint: Determine the known series whose terms past the second give an approximate …
  7. Calculus

    a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure to show the general term of the series. b) Find the radius of convergence of the series. c)Use Lagrange's Remainder Theorem to prove that for x in the interval of …
  8. Calculus 2 (Series)

    Can anyone help me start this problem from beginning to end, along with explanations on how to go about the problem for a better understanding how to do this series problem?
  9. trigonomentry using either exponential or complex

    give the expansion of sin^8@ as a series of cos@ plz help me i only know the normal way of doing that but i do not know how to apply complex number or exponential
  10. math power series(please helpassessment tomorrow)

    The exponential function can be represented as an infinity power series as follows. e^x=1 + x/1! + x^2/2! + x^3/3!+⋯,-∞<x<∞ 1. Calculate e (which is the same as e^1) to 4 significant figures by using as many terms of the …

More Similar Questions