Question

1+4+7+10+....+(3n+1)ma poate ajuta cineva?Multumesc!​

Answer 1

Răspuns:

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

Explicație pas cu pas:

1=3*0+1

4=3*1+1

7=3*2+1

.....

3n+1= 3*n+1

3(0+1+..+n) +1+1+...+1 de n+1  ori

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

Answer 2

nu am operatorul suma, asa ca il voi scrie drept sum( )

1+4+7+10+...+(3n+1)=sum(3k+1)

sum(3k+1)=sum(3k)+sum(1)=3*sum(k)+n

sum(k) e suma gauss, adica:

$\frac{ n(n + 1) }{2}$

si in continuare avem

$3 \times \frac{n(n + 1)}{2} + n$

$\frac{ 3n(n + 1)}{2} + \frac{2n}{2}$

desfacem paranteza si adunam fractiile

$\frac{3 {n}^{2} + 3n + 2n}{2}$

$\frac{3 {n}^{2} + 5n}{2}$