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Martin Knor, Riste Škrekovski and Aleksandra Tepeh

)}}-\frac{n+b}{\sqrt{\left( n+e \right)\left( 2n+f \right)}} \right)=\frac{2\left( e-c \right)+\left( f-d \right)}{4\sqrt{2}}.$$ Proof . Starting from the left side, we derive lim n − ∞ ( n + a ) ( n + b ( n + c ) ( 2 n + d ) − n + b ( n + e ) ( 2 n + f ) ) = lim n → ∞ ( n + a ) ( n + b ) ( n + c ) ( 2 n + d ) ( n + e ) ( 2 n + f ) ⋅ lim n → ∞ ( ( n + e ) ( 2 n + f ) − ( n + c ) ( 2 n + d ) ) = 1 2 lim n → ∞ ( n + e ) ( 2 n + f ) − ( n + c ) ( 2 n + d ) ( n + e ) ( 2 n + f ) + ( n + c ) ( 2 n + d ) = 2 ( e − c ) + ( f − d ) 4 2   . $$\begin{array}{*{35}{l