Se foloseste formula [tex]\displaystyle{ a^{x} \cdot a^{y} = a^{x+y} }[/tex] cat si suma lui Gauss.
[tex]\displaystyle{ 2^{0} \cdot 2^{1} \cdot 2^{2} \cdot .... \cdot 2^{99} \cdot 2^{100} = 2^{0+1+2+.....+99+100} }[/tex]
De la 0 la 100 sunt 101 termeni.
S = (U + P) × Nr T : 2, unde:
- S = suma
- U = ultimul termen
- P = primul termen
- Nr T = numarul de termeni
S = (100 + 0) × 101 : 2
S = 101 × 100 : 2
S = 101 × 50
S = 5050
⇒ [tex]\displaystyle{ 2^{0+1+2+.....+99+100} = 2^{5050} }[/tex]
