a function is defined by f(x)= 1 + 2x + x^2 +2x^3 + x^4 + ... that is, its coefficients are c_2n = 1 and c_2n+1 = 2 for all n>=0 Find the interval of convergence of the series and find an explicit formula for f(x)
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Originally Posted by amiv4 a function is defined by f(x)= 1 + 2x + x^2 +2x^3 + x^4 + ... that is, its coefficients are c_2n = 1 and c_2n+1 = 2 for all n>=0 Find the interval of convergence of the series and find an explicit formula for f(x) We have So applying the root test we get I think its pretty clear that this diverges at both endpoints, so we may conclude that the interval of convergence is . And if you are interested
what other tests could i use besides the root test
Originally Posted by amiv4 what other tests could i use besides the root test Ratio test would also work. You could also note that are the sum of two geometric series, and that each is only convergent on , so the summation of them combined's IOC would be
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