Finding Taylor series of F (x) = LNX at x = 2 How to find the convergence domain How to calculate the open and closed interval of convergence domain

f(x)=lnx=ln(2+(x-2))=ln{2[1+(x-2)/2]}=ln2+ln[1+(x-2)/2];
Then replace X in the expansion of Ln (1 + x) with (x - 2) / 2
The convergence domain of series expansion of Ln (1 + x) is (- 1,1], so the new series is (X-2) / 2 ∈ (- 1,1];
x∈(0,4]

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