How do I evaluate the summation from n=1 to infinity of 1/(1+n^2)
according to the comparison test, this will be a convergent series, but is it possible to find what number it converges to WITHOUT a calculator? If so, how? If not, why not?
according to the comparison test, this will be a convergent series, but is it possible to find what number it converges to WITHOUT a calculator? If so, how? If not, why not?
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well, if you meant if there's a general formula to find the sum, then no. We were able to derive the formula for arithmetic and geometric series, and a few others too, but as for most series, without the help of computer, it's very tedious, if not, nearly impossible, to find the sum because you will need to add MANY MANY MANY terms together to see what the limit of that sum is. All we can do is to determine whether a series is convergent or divergent. If it is convergent, then we can let a computer to find the sum for us. If it's divergent, then there will be no sum.