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sid9221
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[tex] \sum (1-\frac{1}{r})^{r^2} [/tex]
Does this converge or diverge.(r=1..inf)
I have tried the following but do not think it is adequate(or correct for that matter)
[tex] (1-\frac{1}{r})^r (1-\frac{1}{r})^r = (1-\frac{1}{r})^{r^2} [/tex]
and [tex] lim (1-\frac{1}{r})^r -> \frac{1}{e} [/tex]
thats given from a previous part of this question.
So
[tex] lim (1-\frac{1}{r})^r (1-\frac{1}{r})^r -> \frac{1}{e^2} [/tex]
Hence converges ?(As the limit exists)
Does this converge or diverge.(r=1..inf)
I have tried the following but do not think it is adequate(or correct for that matter)
[tex] (1-\frac{1}{r})^r (1-\frac{1}{r})^r = (1-\frac{1}{r})^{r^2} [/tex]
and [tex] lim (1-\frac{1}{r})^r -> \frac{1}{e} [/tex]
thats given from a previous part of this question.
So
[tex] lim (1-\frac{1}{r})^r (1-\frac{1}{r})^r -> \frac{1}{e^2} [/tex]
Hence converges ?(As the limit exists)
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