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**1. The problem statement, all variables and given/known data**

Let Tn(x) be the degree n polynomial of the function sin x at a=0. Suppose you approx f(x) by Tn(x) if abs(x)<=1, how many terms are need (what is n) to obtain an error less than 1/120

**2. Relevant equations**

Rn(x)=M(x-a)^(n+1)/(n+1)!

sin(x)=sum from 0 to ∞ of (-1)^n*x^(2n+1)/(2n+1)!

**3. The attempt at a solution**

For the alternating series test, I plugged in 1 for x in the sin x macluarin series and got 1/(2(n+1)+1)! <= 1/120 and got n=1

Then I used the Taylor's remainder theorem, got 1/(n+1)! <= 1/120 so n=4. why am I getting a different answer from Alternating series estimation theorem?

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