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Sara68
a fost răspuns

S= 2^0+2^1+2^2+2^3+...+2^99

a. demonstrati ca 15 | S
b. Aratati ca S are cel putin 30 cifre

Răspuns :

S=2°+2¹+2²+2³+...+2⁹⁹
2°+2¹+2²+2³=1+3+4+8=15
Deci vom avea:
S=(2°+2¹+2²+2³)+2⁴(1+2+2²+2³)+...+2⁹⁶(1+2+2²+2³)
S=(1+2+2²+2³)(1+2⁴+..+2⁹⁶)
S=15(1+2⁴+..+2⁹⁶)⇒15 | S

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