Hi guys! Is anyone here good at finding the IOC? I have difficult time with this subject so can someone please help me? For example: Infinites Series number 4. How would you know that the IOC is -0.6_< x _< 0.6? I am confuse.
You should use the ratio test. Then take what you have left (ex. (n+1)x/(n+2)) and find what it equals as it approaches infinity. The result will be something like abs(x) so you make it less then 1. So in this case, the ioc would be -1 is less than x is less than 1. Then test the endpoints to see if it is convergent or divergent. If convergent, then the IOC will include that point, and vice versa for divergent.
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You should use the ratio test. Then take what you have left (ex. (n+1)x/(n+2)) and find what it equals as it approaches infinity. The result will be something like abs(x) so you make it less then 1. So in this case, the ioc would be -1 is less than x is less than 1. Then test the endpoints to see if it is convergent or divergent. If convergent, then the IOC will include that point, and vice versa for divergent.
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