Fixing singularities with fun(ctions)

Calculus Level 5

f(x)=tan(x)tan(x+α)f\left( x \right) =\tan { \left( x \right) } \tan { \left( x+\alpha \right) }

Let an{ a }_{ n } denote the nthn^\text{th} smallest positive value of α\alpha that will make f(x)f\left( x \right) continuous over all real values of xx. Evaluate the following sum:

n=1(tan(n)tan(n+an))nan.\sum _{ n=1 }^{ \infty }{ \dfrac { { \left( \tan { ( n ) } \tan { ( n+{ a }_{ n } ) } \right) }^{ n } }{ { a }_{ n } } }.

Round your answer to the nearest three decimal places.

×

Problem Loading...

Note Loading...

Set Loading...