Question

### Gauthmathier7004

Grade 12 · 2021-01-10

The n th term of the Taylor series expansion about x=0 of the function f\left(x\right)=\dfrac {1}{1+2x} is（ ）

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Answer

4.9(568) votes

### Gauthmathier5822

Grade 12 · 2021-01-10

Answer

C

Explanation

\dfrac {1}{1+2x} is the sum of an infinite geometric series with first term 1 and common ratio -2x.

The series is 1-2x+4x^{2}-8x^{3}+16x^{4}-\cdots

The series is 1-2x+4x^{2}-8x^{3}+16x^{4}-\cdots

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