![SOLVED: 3. Estimate pi using the Maclaurin series for arctan(x): 44 The Maclaurin series expansion for the arctangent of x is de- fined for |x| = 1 as (-1)" 2n + SOLVED: 3. Estimate pi using the Maclaurin series for arctan(x): 44 The Maclaurin series expansion for the arctangent of x is de- fined for |x| = 1 as (-1)" 2n +](https://cdn.numerade.com/ask_images/cf37c75538d7440bae02c043366608a2.jpg)
SOLVED: 3. Estimate pi using the Maclaurin series for arctan(x): 44 The Maclaurin series expansion for the arctangent of x is de- fined for |x| = 1 as (-1)" 2n +
SOLVED:Use the Remainder Estimation Theorem and the method of Example 1 to prove that the Taylor series for sinx about x=π/ 4 converges to sinx for all x .
![Dave Richeson on Twitter: "Euler proved that π/4=arctan(1/2)+arctan(1/3), which can be used for computing digits of π (using the arctangent series). I wondered if I could prove it without using a trig Dave Richeson on Twitter: "Euler proved that π/4=arctan(1/2)+arctan(1/3), which can be used for computing digits of π (using the arctangent series). I wondered if I could prove it without using a trig](https://pbs.twimg.com/media/DhXRIQiX0AA9cMz.jpg:large)