Uchburchakli son - bu 1 dan n gacha bo'lgan barcha butun sonlarning yig'indisi. Uchinchi uchburchakli sonni topish uchun tenglama quyidagi formula bilan berilgan: \begin{equation} T_n = \frac{n(n+1)}{2} \end{equation} Ushbu formulani isbotlash uchun biz matematik induksiya yordamida aniqlay olamiz: Asos bosqich: n = 1 uchun tenglama bizga T1 = 1 * (1 + 1) / 2 = 1 beradi, bu birinchi uchburchakli son. Induktiv bosqich: T_k = k * (k + 1) / 2. Endi biz formula n = n + 1, ya'ni T_k = k * (k + 1) uchun ham to'g'ri ekanligini isbotlashimiz kerak.
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