The Pivotals of Mathematics

Algebra Level 5

a+b+c=λa+b+c=\lambda for reals a,b,ca,b,c . We define tn=cyca2n+1\displaystyle t_n= \sum \limits_{cyc} a^{2n+1} for nNn\in \text{N}. Further it's given that t1=λ3t_1={\lambda}^3. Find the value of λ\lambda if n=1tn=16\displaystyle \sum_{n=1}^{\infty} t_n=\frac{1}{6}.

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