Fun with Series 7

Algebra Level 4

f ( x ) = 1 1 + x 2 + ∑ n = 1 ∞ 1 1 + ( x + n ω ) 2 + ∑ n = 1 ∞ 1 1 + ( x − n ω ) 2 f(x)=\frac{1}{1+x^2}+\sum_{n=1}^{\infty}\frac{1}{1+(x+n\omega)^2}+\sum_{n=1}^{\infty}\frac{1}{1+(x-n\omega)^2}

The function f ( x ) f(x) is defined above where ω > 0 ) \omega>0) . Then f ( x ) f(x) is:

Try my fun series .

p e r i o d i c periodic w i t h with p e r i o d period ω \omega n o n p e r i o d i c non periodic p e r i o d i c periodic w i t h with p e r i o d period 2 ω 2 \omega p e r i o d i c periodic w i t h with p e r i o d period ω 2 {\omega}^2

Akshay Sharma by Akshay Sharma , 21, India

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1 solution

C Anshul
Jun 23, 2018

Observe f(x)=f(x+w).

0 Helpful 0 Interesting 0 Brilliant 0 Confused

May you be more explicit, please?

Paul Romero - 9 months, 4 weeks ago

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