求教一个解极限的问题,
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求教一个解极限的问题,
当n趋近于无穷时,(2的n次方加上3的n次方)分之(2的n次方加上3的n+1次方)的极限?
当n趋近于无穷时,(2的n次方加上3的n次方)分之(2的n次方加上3的n+1次方)的极限?
![求教一个解极限的问题,](/uploads/image/z/19458076-4-6.jpg?t=%E6%B1%82%E6%95%99%E4%B8%80%E4%B8%AA%E8%A7%A3%E6%9E%81%E9%99%90%E7%9A%84%E9%97%AE%E9%A2%98%2C)
化简:
[2^n+3^(n+1)]/(2^n+3^n)
=(2^n+3×3^n)/(2^n+3^n)
=(2^n+3^n+2×3^n)/(2^n+3^n)
=1+(2×3^n)/(2^n+3^n)
=1+2/[(2/3)^n+1]
当n趋近于无穷时,(2/3)^n趋近于0
所以lim(n→∞) [1+2/[(2/3)^n+1]=1+2/(0+1 )=3
[2^n+3^(n+1)]/(2^n+3^n)
=(2^n+3×3^n)/(2^n+3^n)
=(2^n+3^n+2×3^n)/(2^n+3^n)
=1+(2×3^n)/(2^n+3^n)
=1+2/[(2/3)^n+1]
当n趋近于无穷时,(2/3)^n趋近于0
所以lim(n→∞) [1+2/[(2/3)^n+1]=1+2/(0+1 )=3