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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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Tutorial Exercise
Find a power series representation for the function. Determine the interval of convergence. (Give your power series representation centered at x = 0.)
1
1-r
f(x)
=
Step 1
We need to express f(x)
=
n = 0
1
2 + x
=
1
in the form
2 + x
Submit Skip (you cannot come back)
1
1-r
and then use the following equation.

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webassign.net skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find a power series representation for the function. Determine the interval of convergence. (Give your power series representation centered at x = 0.) Step 1 1-r We need to express f(x) = Step 2 Step 3 f(x) = f(x) = We can re-write f(x) = Step 4 n=0 = Now, we can use r = - Step 5 1 4+x 1 4 + x -£( n=0 n 1 e f(x) = 4x as f(x) = 1. We can re-write f(x) = Submit We can re-write this as f(x) = Therefore, f(x) = -Σ( n=0 x 1 in the form 4 + X 4 1-r (4) as = ✓ +X --- () n=0 n=0 = 1 1-r Skip (you cannot come back) 1- n=0 and then use the following equation. 1 is equivalent to the following. ✓
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