Fonksiyon

Question

f(x+1)=3x+f(x) ve f(1)=2 olduğuna göre f(21) kactir?

Answer 1

$$f(x+1)-f(x)=3x$$

$$x=1\rightarrow f(2)-f(1)=3.1$$

$$x=2\rightarrow f(3)-f(2)=3.2$$

$$x=3\rightarrow f(4)-f(3)=3.3$$

$$\vdots$$

$$x=20\rightarrow f(21)-f(20)=3.20$$ taraf tarafa toplanırsa

$$f(21)-f(1)=3.(1+2+3+4+...+20)=630\Rightarrow f(21)=632$$ .

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