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shubhamsrg
 4 years ago
infinite summation :
1 + (1/3) + (1.3 / 3.6) + (1.3.5 / 3.6.9) + (1.3.5.7 / 3.6.9.12) ........ = ?
shubhamsrg
 4 years ago
infinite summation : 1 + (1/3) + (1.3 / 3.6) + (1.3.5 / 3.6.9) + (1.3.5.7 / 3.6.9.12) ........ = ?

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shubhamsrg
 4 years ago
Best ResponseYou've already chosen the best response.0so far, my progress has been this much : i started my series from (1/3) ... denom. of nth term is easily (3^n)*(n!) num. of nth term will be 1.3.5.7............ =(1.2.3.4.5...........)/(2.4.6.8........) =( (2n)! )/(2^n * n! ) thus nth term will be (2n)! / (n!)^2 * 6^n or C(2n,n) / 6^n we have to fine its summation from n = 1 to infinity.. but am clueless after this.. will this be even helpful ?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3that's central binomial coefficient ... google for something like it.

shubhamsrg
 4 years ago
Best ResponseYou've already chosen the best response.0well i have googled over,,i got this solution,,but couldnt understand as to why we did that.. it said to compare the summation with (1+x)^n and solve ultimately,,and to my surprise, i got the ans.. if anyone can explain why ?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3it's better to use the generating function directly http://mathworld.wolfram.com/images/equations/CentralBinomialCoefficient/NumberedEquation1.gif

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3http://mathworld.wolfram.com/CentralBinomialCoefficient.html put x=1/6 and get it's value

shubhamsrg
 4 years ago
Best ResponseYou've already chosen the best response.0ohh,,nice !! where does this come from ?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3dw:1349165062856:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3yeah ... I'm just playing around. I've seen that method too ... kinda forget it though.

shubhamsrg
 4 years ago
Best ResponseYou've already chosen the best response.0hmm,,so i should just rote it for the time being !! hmm..anyways ,,thank you.. :)

shubhamsrg
 4 years ago
Best ResponseYou've already chosen the best response.0should i just tag @mukushla @eliassaab

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3dw:1349165603145:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3probably it comes from what google said \[ (1+ax)^k = \sum_{i=0}^k\binom{k}{i}(ax)^i = \sum_{n=0}^\infty \binom{2n}{n}x^k\] since it's infinite k can't be natural number.

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3have to prove that a=4 and k=1/2

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3here is one \[ 1 + {1 \over 3} + {1 \cdot 3 \over 3\cdot 6} + {1\cdot3\cdot 5\over 3\cdot6\cdot9}+...\] \[ (1 + x)^n = 1 + nx + {n(n1) \over 1 \cdot2} x^2 + ....+\infty \] assuming n to be non natural \[ nx = {1 \over 3}\\ {n(n1)\over 1 \cdot2}x^2 = {1 \over 6} \\ \text{ this gives } x={2 \over 3} , n={1 \over 2}\]

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3\[ \left(1  {2 \over 3}\right)^{1 \over 2} = \sqrt{3}\]

shubhamsrg
 4 years ago
Best ResponseYou've already chosen the best response.0hmm..i get the idea i guess.//thanks !! :)

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.3there is bigger idea http://math.stackexchange.com/questions/205898/howtoshowthat1oversqrt14xgeneratesumn0inftybinom2n

shubhamsrg
 4 years ago
Best ResponseYou've already chosen the best response.0ohh yes,,gotcha,,that was really helpful..thanks a ton sir!
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