Question

Calculati limita sirurilor:(photo) vreau punctul c) si daca se poate si g)

Answer 1

Aplici   lema    lui   Stolz   lim   xn+1/yn+1=lim   xn/yn     unde     xn    este    numaratorul    si    xn   numitorul
xn+1-an=1²+2²+...+n²+(n+1)²-1²-2²-...n²=(n+1)²=n²+2n+1
yn+1=(n+1)³-n³=n³+3n²+3n+1-n³=3n²+3n²+3n+1=3n²+3n+1
lim   xn+1/yn+1=(n²+2n+1)/(3n²+3n+1)=1/3
g)   an=xn/yn   yn→∞   Aplici   lema    lui   Stolz
xn+1-xn=1*2+2*3+...+n*(N+1)+(n+1)*(n+2)-1*2-2*3-...-n*(n+1)=(n+1)(n+2)=n²+3n+2
yn+1-yn=(n+1)³-n³=3n²+3n+1
lim xn+1/yn+1= lim (n²+3n+2)/(3n²+3n+1)=1/3

Answer 2

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