Question

For what values of m does the geometric series
1 + (2m - 3) + (2m - 3)^2 + (2m -3)^3 + ... have a limiting sum?

Answer 1

still its not working

Answer 2

Geometric series has first term a=1, and common ratio r = 2m-3. If the summation has a limiting sum, r would be a value between -1 and 1 (both not inclusive). Hence
\begin{eqnarray*}
-1&<&2m-3 \\
2&<&2m \\
1&<&m
\end{eqnarray*}
and
\begin{eqnarray*}
2m-3&<&1 \\
2m&<&4 \\
m&<&2
\end{eqnarray*}
Hence m must be a value between 1 and 2, both not inclusive, in order for the geometric series to have a limiting sum.

Answer 3

I see... Kinda. :P Thanks for your help though! :)