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# Dokazi bez rije ci - matematika.hr

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Dokazi bez rijeci
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Sume
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Suma prvih n neparnih brojeva
1 + 3 + · · · + (2n− 1) = n2
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Suma prvih n neparnih brojeva
1 + 3 = 22
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Suma prvih n neparnih brojeva
1 + 3 + 5 = 32
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Identitet za sumu prvih n brojeva
Sn = 1 + 2 + · · · + n
8Sn + 1 = (2n + 1)2
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Identitet za sumu prvih n brojeva
8 · 1 + 1 = 32
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Identitet za sumu prvih n brojeva
8 · (1 + 2) + 1 = 52
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Identitet za sumu prvih n brojeva
8 · (1 + 2 + 3) + 1 = 72
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Suma geometrijskog reda I
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Suma geometrijskog reda II
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Trisekcija kuta u beskonacno koraka
1
2
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Ekvipotentnost
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#(a, b) = #R
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Identiteti za trokut
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Pitagorin poucak
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Kosinusov poucak
γ
(a + c)(a− c) = (2a cos γ − b)b ⇒ c2 = a2 + b2 − 2ab cos γ
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Suma arkus tangensa I
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Suma arkus tangensa II
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Nejednakosti
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A-G nejednakost I
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Nejednakost sredina
a b
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A-G nejednakost II-Lema
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A-G nejednakost II
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Napierova nejednakost-prvi dokaz
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Napierova nejednakost-drugi dokaz
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Eksponencijalna nejednakost AB > BA za e ≤ A < B
y = nAx
y = nBx
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Limesi
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lim n→∞

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Parcijalna integracija
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Parcijalna integracija v
r = g(a)
a −
b∫
a
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Dandelinove kugle
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Dandelinove kugle
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