Do you know its property? -11

Algebra Level 5

If the fundamental period of a continuous non-zero function \(f(x)\) satisfying

\[\large f(x+1)+f(x-1)=\sqrt{\pi}.f(x)\]

is \(a_1a_2a_3a_4a_5a_6a_7.b_1b_2b_3b_4b_5b_6b_7\), find the value of \(\displaystyle \sum_{i=1}^7 (a_i+b_i)\).

Assumptions:

  • Round off your answer up to 7 decimal places.

  • \(0 \leq a_1,a_2,a_3,a_4,a_5,a_6,a_7,b_1,b_2,b_3,b_4,b_5,b_6,b_7 \leq 9\)

  • \(\{a_1,a_2,a_3,a_4,a_5,a_6,a_7,b_1,b_2,b_3,b_4,b_5,b_6,b_7\} \in \mathbb{Z}\)

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