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27/12/2021 12:42 pm
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Find the value of \(\frac{1}{1+x}\) + \(\frac{2}{1 + x^2}\) + \(\frac{2^2}{1 + x^4}\)+ .....\(\frac{2^{100}}{1+x^{200}}\)
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27/12/2021 12:46 pm
\(\frac{1}{1+x}\) + \(\frac{2}{1 + x^2}\) + \(\frac{2^2}{1 + x^4}\)+ .....\(\frac{2^{100}}{1+x^{200}}\)
= \(\frac{1}{1-x}\) + \(\frac{1}{1 + x}\) + \(\frac{2}{1 + x^2}\)+\(\frac{2^2}{1 + x^4}\)+ .....\(\frac{2^{100}}{1+x^{200}}\) - \(\frac{1}{1-x}\)
= \(\frac{2}{1-x^2}\) + \(\frac{2}{1+x^2}\) + \(\frac{2^2}{1-x^4}\)+.....+\(\frac{2^{100}}{1+x^{200}}\) - \(\frac{1}{1-x}\)
= \(\frac{2^2}{1-x^4}\) + \(\frac{2^2}{1+x^4}\) +.....\(\frac{2^{100}}{1+x^{200}}\) - \(\frac{1}{1-x}\)
In similar way we will get
\(\frac{2^{100}}{1+x^{200}}\)-\(\frac{1}{1-x}\)
This post was modified 3 years ago by Reyana09