gauss

toaderflorentina · Mesaj de **toaderflorentina** » 24 Sep 2014, 09:40

5+6+7+8+9+10+11+12=
multumesc

tata2008 · Mesaj de **tata2008** » 25 Sep 2014, 06:47

toaderflorentina scrie:5+6+7+8+9+10+11+12=
multumesc

$\rm{\Large\bl\\ I. Forma general\breve{a} a lui Gauss, este: 1+2+3+ ... + n = n *(n+1) : 2 \\ II. Ca s\breve{a} avem aceast{a} form\breve{a} , proced\breve{a}m astfel:\\ 5+6+7+8+9+10+11+12 +(1+2+3+4) - (1+2+3+4) \\ adic\breve{a} \underbrace{1+2+3+4+5+6+7+8+9+10+11+12}_{12*13:2=\fbox{78}} - (\underbrace{1+2+3+4}_{4*5 :2=\fbox{10}}) = 78-10 = ... ;\\ Sau: S= 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + ! (avem 12-5 + 1 =8 termeni)\\ \underline{S= 12 +11 +10 +9 + 8 + 7 + 6 + 5 }\\ 2S= \underbrace{17+17+ .........................................................+17}_{17 de 8 ori}\\ S = 17*8:2= 68 ;$

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