If ... Calculate

May 2009
596
31
ALGERIA
If : \(\displaystyle f(x)=x^{(x+1)}\times (x+2)x^{(x+3)}\)
Calculate : \(\displaystyle f(0)-f(-1)+f(-2)-f(-3)\)
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
If : \(\displaystyle f(x)=x^{(x+1)}\times (x+2)x^{(x+3)}\)
Calculate : \(\displaystyle f(0)-f(-1)+f(-2)-f(-3)\)
\(\displaystyle x^{x+1}x^{x+3}=x^{x+1+x+3}=x^{2x+4}\)

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