Question

Se considera numerele a=(1+1/2)×(1+1/3)×...×(1+1/10) si b=(1-1/2)×(1-1/3)×....×(1-1/10). Sa se arate ca a=11/2 si b= 1/10.​

Answer 1

Răspuns:

Explicație pas cu pas:

a = (1 + 1/2) × (1 + 1/3) × ... × (1 + 1/10)

= 3/2 × 4/3 × 5/4 × 6/5 × 7/6 × 8/7 × 9/8 × 10/9 × 11/10 = 11/2

b = (1 - 1/2) × (1 - 1/3) × .... × (1 - 1/10)

= 1/2 × 2/3 × 3/4 × 4/5 × 5/6 × 6/7 × 7/8 × 8/9 × 9/10 = 1/10