Question

23 Calculaţi: 1 a radical din 2(1+2+3+4+...+24)×(1/1*2 +1/2*3 +1/3*4 +..... +1/24*25)​

Answer 1

Răspuns:

24/25

Explicație pas cu pas:

1+2+3+...+n=n(n+1)/2

1/1*2=1/1 – 1/2, 1/2*3=1/2 – 1/3

1/[n(n+1)]=1/n  - 1/(n+1)

√ [2(1+2+3+4+...+24)×(1/1*2 +1/2*3 +1/3*4 +..... +1/24*25)]

=√ [2(24*25)/2 ×(1/1-1/2 +1/2-1/3 +1/3-1/4 +..... +1/24-1/25)]

=√ [(24*25) ×(1/1-1/25)]

=√ [(24*25) ×(24/25)]

=24/25