37b-cauldron-and-shroompath solutions

[kbokis]

37ος ΠΔΠ _ Μονοπάτι μανιταριών (shroompath) - Λύση.pdf

[Dim131]

$$\begin{aligned} p(k+1) & = p(k) + f(k+1) \\ & = 2^{k+1}\cdot (k-1)+2 + 2^{k+1} \cdot (k+1) \\ & = 2^{k+1}\cdot k - 2^{k+1} + 2 + 2^{k+1}\cdot k + 2^{k+1} \\ & = 2^{k+1}\cdot k - \cancel{2^{k+1}} + 2 + 2^{k+1}\cdot k + \cancel{2^{k+1}} \\ & = 2^{k+1}\cdot k + 2^{k+1}\cdot k + 2 \\ & = 2\cdot 2^{k+1} \cdot k + 2 \\ & = 2^{k+2}\cdot k +2, \end{aligned}$$

[kbokis]

Αρκετά πιο όμορφο. Ευχαριστώ