作业帮[(2/3)+(2/3)^2+(2/3)^3+(2/3)^4+……]证明其结果为什么等于2
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[(2/3)+(2/3)^2+(2/3)^3+(2/3)^4+……]证明其结果为什么等于2
[(2/3)+(2/3)^2+(2/3)^3+(2/3)^4+……]证明其结果为什么等于2
[(2/3)+(2/3)^2+(2/3)^3+(2/3)^4+……]证明其结果为什么等于2
设[(2/3)+(2/3)^2+(2/3)^3+(2/3)^4+……+(2/3)^n]=s
则[(2/3)^2+(2/3)^3+(2/3)^4+……+(2/3)^(n+1)=(2/3)s
(2/3)-(2/3)^(n+1)=1/3s
s=2-2*(2/3)^n
取极限n趋近于无穷大
2*(2/3)^n趋近于0
所以s趋近于2
运用等比数列公式:
得[(2/3)+(2/3)^2+(2/3)^3+(2/3)^4+……]
=2/3*[1-(1/3)^n]*3
=2*[1-(1/3)^n]
当n趋向无穷大时,(1/3)^n趋向于0,原式值即为2