数列的极限题
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数列的极限题
数列的极限题
数列的极限题
lim(n→∞)[(2+3)/4+(2^2+3^2)/4^2+……+(2^n+3^n)/4^n]
=lim(n→∞){[(2/4)+(2/4)^2+(2/4)^3+...+(2/4)^n]+[(3/4)+(3/4)^2+(3/4)^3+.+(3/4)^n]}
=lim(n→∞){[1-(1/2)^n]+3[1-(3/4)^n]}
=lim(n→∞)[4-(1/2)^n-3*(3/4)^n]
因此,当n趋于正无穷时,所求极限为 4 .
1/2/(1-1/2)+3/4/(1-3/4)=4