[tex]\displaystyle\bf\\Se~da:\\\\f:R\to R, f(x)=-10x-6\\\\Se~cere:\\\\f(16)+f(17)+...+f(36)=?\\\\Rezolvare:\\\\Calculam~numarul~de~termeni~de~la~16~pana~la~36:\\\\n=36-16+1=20+1=\boxed{\bf21~de~termeni}\\\\f(16)=-10\cdot16-6\\f(17)=-10\cdot17-6\\............................\\f(36)=-10\cdot36-6\\\textbf{- - - - - - - - - - - - - - Adunam:}[/tex]
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[tex]\displaystyle\bf\\f(16)+f(17)+...+f(36)=\\\\=(-10\cdot16-6)+(-10\cdot17-6)+...+(-10\cdot36-6)=\\Descompunem~in~2~sume:\\=(-10\cdot16)+(-10\cdot17)+...+(-10\cdot36)+\underbrace{\bf(-6)+(-6)+...+(-6)}_{21~de~(-6)}=\\\\=-10\cdot(16+17+...+36)+21\cdot(-6)=\\\\=-10\cdot\frac{21(36+16)}{2}+ 21\cdot(-6)=\\\\=-10\cdot\frac{21\cdot52}{2}-126=\\\\=-10\cdot21\cdot26-126=\\\\=-10\cdot546-126=\\\\=-5460-126=\boxed{\bf-5586}[/tex]
