Question

the interval for which the series 1+(x-1)+(x-1)^2+.........+≠ may be summed is

Answer 1

it's upto infinity

Answer 2

\[\sum(x-1)^n\]
\[\lim_{n\to inf}\frac{(x-1)^{n+1}}{(x-1)^n}\]
\[\lim_{n\to inf}(x-1)\]
\[|x-1|\lim_{n\to inf}1=|x-1|\]
\[\|x-1|<1\]
\[-1<x-1<1\]
\[0<x<2\]