Do you know its property? -11

Algebra Level 5

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

f(x+1)+f(x1)=π.f(x)\large f(x+1)+f(x-1)=\sqrt{\pi}.f(x)

is a1a2a3a4a5a6a7.b1b2b3b4b5b6b7a_1a_2a_3a_4a_5a_6a_7.b_1b_2b_3b_4b_5b_6b_7, find the value of i=17(ai+bi)\displaystyle \sum_{i=1}^7 (a_i+b_i).

Assumptions:

  • Round off your answer up to 7 decimal places.

  • 0a1,a2,a3,a4,a5,a6,a7,b1,b2,b3,b4,b5,b6,b790 \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

  • {a1,a2,a3,a4,a5,a6,a7,b1,b2,b3,b4,b5,b6,b7}Z\{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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