Series Proof Help: Proving |ln 2| & |sin x|

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(1) Show that |ln 2 - ƩNn=1 ((-1)n-1)(1/n)| ≤ 1/(N+1)
(2) Show that |sin x - ƩNn=0 ((-1)n)/(2n+1)!| ≤ |x|2N+2/(2N+2)!


I really don't know where to start. should I change the sums to series first then work my way through? Please help!
 
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Those are alternating series. The error bound is just the next element of the series.
 
ohhhhh wow now i see. thanks so much!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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