Least odd natural number

Algebra Level 5

\[\begin{cases} A_n=\left(\frac{3}{4}\right)-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^3+\cdots+(-1)^{n-1}\left(\frac{3}{4}\right)^n \\ B_n=1-A_n \end{cases} \]

Find the least odd positive integer, \(n_0\) such that \(B_n>A_n \) for all \( n \geq n_0\).


You can try my other Sequences And Series problems by clicking here : Part II and here : Part I.
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