Least odd natural number

Algebra Level 5

{An=(34)(34)2+(34)3++(1)n1(34)nBn=1An\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, n0n_0 such that Bn>AnB_n>A_n for all nn0 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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