Question

2^0×2^1×2^2×....×2^99×2^100
VĂ ROG MUUUUUUUUUUULLLLLLLTTTTTT DAU COROANĂ!!!!!!!!!​

Answer 1

Se foloseste formula $\displaystyle{ a^{x} \cdot a^{y} = a^{x+y} }$ cat si suma lui Gauss.

$\displaystyle{ 2^{0} \cdot 2^{1} \cdot 2^{2} \cdot .... \cdot 2^{99} \cdot 2^{100} = 2^{0+1+2+.....+99+100} }$

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

⇒ $\displaystyle{ 2^{0+1+2+.....+99+100} = 2^{5050} }$