আদৌ কি বের করা সম্ভব?
summation of series[own!!!!????]
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Tahmid Hasan
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$7+13+23+37+55+77+103+133+167+205+........+18055+18437+18823$
আদৌ কি বের করা সম্ভব?
আদৌ কি বের করা সম্ভব?
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Re: summation of series[own!!!!????]
Identity:
And if I'm correct, the third number should be $21$.\[\sum^n_{i=0} f_i = f_{n+2}-1\]
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Tahmid Hasan
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Phlembac Adib Hasan
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Re: summation of series[own!!!!????]
What are you talking about?.I don't understand.Do you want to find $\sum_{k=1}^{n}2(k^2+1)+3$?
$\sum_{k=1}^{n}2(k^2+1)+3$
$\Rightarrow (2\sum_{k=1}^{n}k^2)+5n$
$\Rightarrow \frac {1} {3} [2n^3+3n^2+n]+5n $
$\sum_{k=1}^{n}2(k^2+1)+3$
$\Rightarrow (2\sum_{k=1}^{n}k^2)+5n$
$\Rightarrow \frac {1} {3} [2n^3+3n^2+n]+5n $
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Tahmid Hasan
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Re: summation of series[own!!!!????]
i just showed the generalized form of every term.now it is quite easy to find the sum.(just like you didPhlembac Adib Hasan wrote:What are you talking about?.I don't understand.Do you want to find $\sum_{k=1}^{n}2(k^2+1)+3$?
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Re: summation of series[own!!!!????]
How?Tahmid Hasan wrote:my calculation
$n$th term $2(n^2+1)+3$
Last edited by *Mahi* on Sat Dec 31, 2011 11:52 am, edited 1 time in total.
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nafistiham
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Re: summation of series[own!!!!????]
*Mahi* wrote:How in earth?Tahmid Hasan wrote:my calculation
$n$th term $2(n^2+1)+3$
well i have found that we get the number quite rightly.what's the problem here ?
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: summation of series[own!!!!????]
The difference are $4n+2$, so it can be easily derived. I meant that.
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nafistiham
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Re: summation of series[own!!!!????]
*Mahi* wrote:The difference are $4n+2$, so it can be easily derived. I meant that.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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