Xn=(3n+2)/(5n-1) xn+1=(3n+3+2)/(5n+5-1)=(3n+5)/(5n+4)
xn+1-xn=(3n+5)/(5n+4)-(3n+2)/(5n-1)=[(3n+5)(5n-1)-(3n+2)(5n+4)]/(5n+4)/(5n-1)
(3n+5)(5n-1)-(3n+2)(5n+4)=15n²+25n-3n-5-15n²-10n-12n-8=-13
xn+1-xn=-13/(5n+4)/(5n-1) <0 монотонно убывает<br>lim xn n→∞ =3/5 ограничена.
xn=1+2+........+ n xn+1-xn=n+1 монотонно возрастает, неограниченна.
xn=(2n+(-1)ⁿ)/(4n-3) xn+1/xn=(2n+(-1)ⁿ⁺¹)(4n-3)/(2n+(-1)ⁿ)(4n+1)
n=2k xn+1/xn=(2n-1)(4n-3)/(2n+1)(4n+1).>1
n=2k+1 xn+1/xn=(2n+1)(4n-3)/(2n-1)(4n+1)<1 не возрастает и не<br>убывает.
lim xn n→∞ (2n+(-1)ⁿ)/(4n-3) =lim n→∞2n/(4n-3) =2/4=0.5 ограничена