summation notion beginning at n=1... [(-1)^n]/n No calculator use please. Any way to figure where it converges?
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The power series for is . It converges when |x|<1 but also when x=1 (though this is harder to prove).
Uh... what? I don't understand. My series isn't even a power series. I'm not asking whether it converges, but where it converges.
Originally Posted by Kaitosan Uh... what? I don't understand. My series isn't even a power series. I'm not asking whether it converges, but where it converges. He's actually telling you how to find the sum (which is usually difficult to do in closed form) Try substituting .
Gotcha. Thanks guys.
Originally Posted by Opalg The power series for is . It converges when |x|<1 but also when x=1 (though this is harder to prove). As I thought about that, I actually think you meant... Since my series start at n=1. Also, I think I can use the expression since it barely converges to lol. Right?
Yes, it is . Here's why: Start with the alternating geometric series: Now make each side negative: Integrate both sides: So Plugging in gives you
Heh yeah. Thank you redsoxfan! This information is kinda new to me.
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