Jacobsthal-Geometric Series

Algebra Level 5

Jn={0if n=0;1if n=1;Jn1+2Jn2if n>1.\text{J}_{n}=\begin{cases} 0 \quad & \text{if}~n=0; \\ 1 \quad & \text{if} ~ n=1; \\ \text{J}_{n-1}+2\text{J}_{n-2} \quad & \text{if}~n>1.\end{cases}

Jacobsthal Numbers are defined by the recurrence relation as described above. Evaluate: n=0Jn10n+1  .\displaystyle \sum_{n=0}^{\infty} \dfrac{\text{J}_{n}}{10^{n+1}} \; .

If the value of the above expression is in the form A1A^{-1}, find AA.


Inspiration

×

Problem Loading...

Note Loading...

Set Loading...