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These are questions asked by Lonely

how to solve

-x^8*a^4+48*z^4+48*x^7*a+8*z*x^6*a-1 = 0

for a

i tried


solve(-x^8*a^4+48*z^4+48*x^7*a+8*z*x^6*a-1 = 0, a)


and got



How to solve this receurrence relation with maple


a[k] := (2/5)*a[k-1]*ln((1/10)*(exp(1)*x/a[k-1])^10)/ln(10^a[k-1]*(exp(1))^4)


I found various methods, as listen here http://en.wikipedia.org/wiki/Recurrence_relation, to solve recurrsion relation. For example, methods of undertermined coefficients


But how to use these to solve the the above recursive relation.



let us consider the series


y = a_0 - sum(a_i,i=1..n)


here the terms a_i are defined recurrsively as follows


a_i = (a_(i-1) -4*ln(x)/ln(10) + 4/10 + 4*ln(a_(i-1)) )/ ( 1+ 4/(a_(i-1) * ln(10)))


a[n] := (a[n-1]-4*ln(x)/ln(10)+4*(1/10)+4*ln(a[n-1]))/(1+4/(a[n-1]*ln(10)))


how can i program this in maple. so i can...


what is the general sum formula for the following seires (we may notice from these few terms it has a pattern)



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