abhas
Active member
![paper - Find sum of series [solved] Vide](https://2img.net/i/fa/vide.gif) |  Subject: Find sum of series [solved] Wed Aug 27, 2008 6:32 pm | |
| ![paper - Find sum of series [solved] 45d3d651-7a78-45d7-93a0-18d0cff43446](https://2img.net/h/www.goiit.com/equations/2008/8/26/45d3d651-7a78-45d7-93a0-18d0cff43446.png)
![paper - Find sum of series [solved] C2b38e63-569e-4812-9125-68a9f04fd3d1](https://2img.net/h/www.goiit.com/equations/2008/8/26/c2b38e63-569e-4812-9125-68a9f04fd3d1.png)
By Euler's formula ![paper - Find sum of series [solved] B1f202f84bf08c0d914c1b64336301d4df51529c](https://2img.net/h/alt2.mathlinks.ro/Forum/latexrender/pictures/b/1/f/b1f202f84bf08c0d914c1b64336301d4df51529c.gif) .
Consider, ![paper - Find sum of series [solved] 4dcdca55829fb101f51fce2913e72a6302b44534](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/4/d/c/4dcdca55829fb101f51fce2913e72a6302b44534.gif) .
Then, the sum in 1) of the problem is ![paper - Find sum of series [solved] 7d6dca96c069e55028da2fcee028bc3c2ab4bd8f](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/7/d/6/7d6dca96c069e55028da2fcee028bc3c2ab4bd8f.gif) , and that in 2) is ![paper - Find sum of series [solved] 54b72761e3933cfabf668afcc338b806fee01c2b](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/5/4/b/54b72761e3933cfabf668afcc338b806fee01c2b.gif) .
Here ![paper - Find sum of series [solved] 1582eb1c5e286946e943fabdbb8607c13e419dce](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/1/5/8/1582eb1c5e286946e943fabdbb8607c13e419dce.gif) and ![paper - Find sum of series [solved] 6f4afef880cdf22748849a4667bf04cae0e90deb](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/6/f/4/6f4afef880cdf22748849a4667bf04cae0e90deb.gif) represents, respectively, the real and the imaginary part of the complex number ![paper - Find sum of series [solved] 395df8f7c51f007019cb30201c49e884b46b92fa](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/3/9/5/395df8f7c51f007019cb30201c49e884b46b92fa.gif) .
Now,
![paper - Find sum of series [solved] 3c59d6524a063b28824bdc5018545d950f630952](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/3/c/5/3c59d6524a063b28824bdc5018545d950f630952.gif)
![paper - Find sum of series [solved] 5acdd38b751e838f3b67d837ecda896c4ef2e444](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/5/a/c/5acdd38b751e838f3b67d837ecda896c4ef2e444.gif)
![paper - Find sum of series [solved] 7c12f3979436466ef704cacaa13eac1cfb6afe1f](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/7/c/1/7c12f3979436466ef704cacaa13eac1cfb6afe1f.gif)
where I have used the fact that, for ![paper - Find sum of series [solved] Cb21cc47aa5d2b3dd1eeb543d57b3307fa0a7f13](https://2img.net/h/alt2.mathlinks.ro/Forum/latexrender/pictures/c/b/2/cb21cc47aa5d2b3dd1eeb543d57b3307fa0a7f13.gif) ,
![paper - Find sum of series [solved] D8b8f976d5d1061addbc504df0d37715464a8113](https://2img.net/h/alt2.mathlinks.ro/Forum/latexrender/pictures/d/8/b/d8b8f976d5d1061addbc504df0d37715464a8113.gif) .
Now, we see that ![paper - Find sum of series [solved] 7c962b50520dc6ce7636eec27f5b56f970948bbd](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/7/c/9/7c962b50520dc6ce7636eec27f5b56f970948bbd.gif)
![paper - Find sum of series [solved] B8cbc357d018810d02fcee78901fc4475bbb76f4](https://2img.net/h/alt2.mathlinks.ro/Forum/latexrender/pictures/b/8/c/b8cbc357d018810d02fcee78901fc4475bbb76f4.gif)
So we get, ![paper - Find sum of series [solved] 60bbbe3ee98a5ed67d47cc03edb5240d04aaade1](https://2img.net/h/alt1.mathlinks.ro/Forum/latexrender/pictures/6/0/b/60bbbe3ee98a5ed67d47cc03edb5240d04aaade1.gif) and ![paper - Find sum of series [solved] Ab0f9e4e590f619b83f24f002ba33d9360d111b7](https://2img.net/h/alt2.mathlinks.ro/Forum/latexrender/pictures/a/b/0/ab0f9e4e590f619b83f24f002ba33d9360d111b7.gif) .
Accordingly,
1) ![paper - Find sum of series [solved] A34d8c44b051c2f9fc60a39a018ec858ba60485f](https://2img.net/h/alt2.mathlinks.ro/Forum/latexrender/pictures/a/3/4/a34d8c44b051c2f9fc60a39a018ec858ba60485f.gif)
2) ![paper - Find sum of series [solved] B3257286bbe23d5e74f6d8f713c4cc74bed01995](https://2img.net/h/alt2.mathlinks.ro/Forum/latexrender/pictures/b/3/2/b3257286bbe23d5e74f6d8f713c4cc74bed01995.gif) |
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sadanand
Guest
| | Subject: model paper of I.sc 2009 from U.p board Wed Jan 14, 2009 10:51 pm | |
| Dear sir/madam
i need model paper of subject Hindi/phy/chem/bio and eng
with answer if its possible please help me & send me an my email
my email address is given below
|
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samuel007
| | Subject: Re: Find sum of series [solved] Thu Feb 19, 2009 12:10 pm | |
| [fla3.png" alt="Like a Star @ heaven" smilieid="22" />       |
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