conceptual limit problem maybe....!!

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The value of lim (n -> âˆž) [sum (r varies 1 to n) {1/2^r}], where [.] -> G.I.F is ................

#Mathematics #Algebra

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6 Answers

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Aditya Bhutra ·2012-06-02 11:29:19

S_{n} = \sum_{1}^{n}{\frac{1}{2^{r}}}

S_{n} = \frac{1}{2} + \frac{1}{2^{2}} + .... + \frac{1}{2^{n}}

S_{n} = \frac{1}{2}*\frac{1- (1/2)^{n}}{1-(1/2)}

S_{n} = 1- (1/2)^{n}

0<S_{\propto } <1

\left[ S_{\propto }\right] =0

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Manish Shankar So the answer is 1-0=1
Upvote·0· Reply ·2012-06-12 23:38:08
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36

rahul ·2012-06-02 11:34:15

thanku....!!

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sougata nag ·2012-06-03 00:30:25

ya i had a gross mistake but are u sure the limit isn't 1?

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262

Aditya Bhutra ·2012-06-03 06:02:11

it is 0

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1357

Manish Shankar ·2012-06-12 23:39:31

another way

S=(1/2)+(1/2²).....âˆž

so it is infinite GP.

S=a/(1-r)=(1/2)/(1-1/2)=1

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2305

Shaswata Roy ·2012-06-13 20:09:49

It's not 0 it's 1.In the inequality you had given , you didn't consider n=âˆž.

As nâ†’âˆž (1/2)ⁿâ†’0
Hence 0<S_nâ‰¤1
And S_âˆž=1

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