\[\large{{ a }_{ 1 }^{ 2 }{ a }_{ 2 }+{ a }_{ 2 }^{ 2 }{ a }_{ 3 }+......+{ a }_{ 100 }^{ 2 }{ a }_{ 1 }}\]

Let \(a_{i}\) represent non-negative real numbers such that \(a_{1}^{2}+a_{2}^{2}+......+a_{100}^{2}=1\) then find the maximum value of above expression. Answer upto 4 decimal places

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