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idku
 one year ago
How do I write these fractions as a series (if possible)?
idku
 one year ago
How do I write these fractions as a series (if possible)?

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idku
 one year ago
Best ResponseYou've already chosen the best response.0\(\large\color{black}{ \displaystyle \frac{ 1 }{2\times 3 \times 4} \frac{ 1 }{4\times 5 \times 6}+\frac{ 1 }{6\times 7 \times 8}\frac{ 1 }{8\times 9 \times 10}~+.... }\) and this pattern continues like this.

idku
 one year ago
Best ResponseYou've already chosen the best response.0\(\Large\color{black}{ \displaystyle \sum_{n=1}^\infty ~\left[\frac{\left(½(½)(1)^n\right)}{(n+1)(n+2)(n+3)}~\right] }\) but there is one problem here

idku
 one year ago
Best ResponseYou've already chosen the best response.0I need to have: positive output, when n=1 negative output, when n=3 positive output, when n=5 negative out, when n=7 so on....

idku
 one year ago
Best ResponseYou've already chosen the best response.0I need alternation, but regular (1)\(^n\) wouldn't suffice here....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sum_{n=1}^{\infty}\frac{ \left( 1 \right)^{n+1} }{ 2n \left( 2n+1 \right)\left( 2n+2 \right) }\]

idku
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah! I thought of 2n in the beginning, but for some reason I thought it was wrong... clearly, 2*3*4 then 4*5*6 and on also, the alternation is there. THANKS !!!!

idku
 one year ago
Best ResponseYou've already chosen the best response.0So, I can say: \(\large \displaystyle \pi =3+\sum_{n=1}^{\infty}\frac{ 4\left( 1 \right)^{n+1} }{ 2n \left( 2n+1 \right)\left( 2n+2 \right) }\)

idku
 one year ago
Best ResponseYou've already chosen the best response.0this is why i wanted that series representation. thanks once again:)
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