Question

Sn=4+7+...+(3n+1) va rog dau coroana

Answer 1

Sn=4+7+...+(3n+1)
Sn=(3n+1)+(3n-2)+...+4
2Sn=(4+3n+1)+(3n-2+7)+...+(3n+1+4)
2Sn=(3n+5)+(3n+5)+....+(3n+5)
Nr termeni=(3n+1-4)/(7-4)+1=(3n-3)/3+1=n-1+1=n
2Sn=n(3n+5)
Sn=n(3n+5)/2

Answer 2

Sn=3*1+1+3*2+1+..+3n+1=3(1+2+...+n)+ (1+1...+1) de n ori=

3n(n+1)/2 +n=3n(n+1)/2+2n/2=(n/2)* (3n+3+2)=n(3n+5)/2
se verifica usor pt n=2 si n=3...
prin inductie nu mai fac, pt.ca nu s-a cerut