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a fost răspuns

Aflati x din :
a) 1+2+2²+2³+........+2ˣ=2⁶⁴-1
b) 99+2(1+2+3+.....+x)=99²

Răspuns :

Spidie
a) 1+2+2²+2³+........+2ˣ=2⁶⁴-1
2⁰+2¹+2²+2³+...+2⁶³= 2⁶⁴-1
x=2⁶³
dupa formula : 2⁰+2¹+2²+...2ⁿ= 2ⁿ⁺¹  -1

b) 99+2(1+2+3+.....+x)=99²
99+2*[x*(x+1)]/2=99²
99+x*(x+1)= 99²
x*(x+1)=99²-99
x*(x+1)=99*(99-1)
x*(x+1)=98*99
x=98

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