作业帮求下列式子的极限
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求下列式子的极限
求下列式子的极限
求下列式子的极限
不懂再问
1) 原式= lim(n→∞) {[1- (1/2)^(n+1)]/2 } / {[1- (1/3)^(n+1)]/(2/3) }
= [ 2- (1/2)^n ] / [ (3/2) - 2*(1/3)^n ]
= 2/(3/2)
= 4/3
2) 原式= lim(x→1) [(x+x²+...
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1) 原式= lim(n→∞) {[1- (1/2)^(n+1)]/2 } / {[1- (1/3)^(n+1)]/(2/3) }
= [ 2- (1/2)^n ] / [ (3/2) - 2*(1/3)^n ]
= 2/(3/2)
= 4/3
2) 原式= lim(x→1) [(x+x²+……+x^n)(x-1) - n(x-1)] / (x-1)²
= lim(x→1) [(x^(n+1) - x - n(x-1)] / (x-1)²
= lim(x→1) [(x^(n+1) - 1 ] / (x-1)²
= ∞
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