# Power Series Expansion for Tangent Function/Mistake

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## Contents

## Source Work

1992: George F. Simmons: *Calculus Gems*:

- Chapter $\text {B}.20$: The Bernoulli Numbers and some Wonderful Discoveries of Euler
- The Power Series for the Tangent

This mistake can be seen in the $1992$ edition as published by McGraw-Hill: ISBN 0-07-057566-5

## Mistake

*Based on our knowledge of the Bernoulli numbers, the first few terms of the [ Power Series Expansion for Tangent Function ] are easy to calculate explicitly,*

- $\tan x = x + \dfrac 1 3 x^3 + \dfrac 2 {15} x^5 + \dfrac {17} {315} x^7 + \dfrac {67} {2835} x^9 + \cdots$

The numerator of the coefficient for $x^9$ is in fact $62$, not $67$.

The correct calculation can be found in Power Series Expansion for Tangent Function/Sequence.

## Also see

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.20$: The Bernoulli Numbers and some Wonderful Discoveries of Euler