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Chapter 8: Q. 17 (page 692)

Use an appropriate Maclaurin series to find the values of the series in Exercises 17鈥�22.
鈭�k=0鈭�-蟺kk!

Short Answer

Expert verified

The required answer is鈭�k=0鈭�-蟺kk!=e-蟺

Step by step solution

01

Step 1. Given Information

The given series is鈭�k=0鈭�-蟺kk!

02

Step 2. Explanation

The maclaurin series for the function f(x)=exisex=鈭�k=0鈭�1k!xk

So, the given series is the maclaurin series for exatx=-蟺

Since, 鈭�k=0鈭�1k!ek=ex

Thus,鈭�k=0鈭�-蟺kk!=e-蟺

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Most popular questions from this chapter

Prove that if (-p,p]is the interval of convergence for the series 鈭�k=0鈭�鈥�akxk, then the series converges conditionally at p.

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