Engineering Mathematics Calculus Fourier Series

The series \(\mathop \sum \limits_{{\rm{m}} = 0}^\infty \frac{1}{{{4^{\rm{m}}}}}{\left( {{\rm{x}} - 1} \right)^{2{\rm{m}}}}\) converges for

1
\( - 2 < {\rm{x}} < 2\)
2
\( - 1 < {\rm{x}} < 3\)
3
\( - 3 < {\rm{x}} < 1\)
4
\({\rm{x}} < 3\)

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