1. If ... Calculate

If : $f(x)=x^{(x+1)}\times (x+2)x^{(x+3)}$
Calculate : $f(0)-f(-1)+f(-2)-f(-3)$

2. Originally Posted by dhiab
If : $f(x)=x^{(x+1)}\times (x+2)x^{(x+3)}$
Calculate : $f(0)-f(-1)+f(-2)-f(-3)$
$x^{x+1}x^{x+3}=x^{x+1+x+3}=x^{2x+4}$

$x^{2x+4}(x+2)=x^{2x+4}x+2x^{2x+4}=x^{2x+4+1}+2x^{2 x+4}=x^{2x+5}+2x^{2x+4}$

3. Suggestion

$0^4=0$
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