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A sequence of 2xx2 matrices {M(n)} is de...

A sequence of `2xx2` matrices `{M_(n)}` is defined as follows `M_(n)=[((1)/((2n+1)!),(1)/((2n+2)!)),(sum_(k=0)^(n)((2n+2)!)/((2k+2)!), sum_(k=0)^(n)((2n+1)!)/((2k+1)!))]` then `lim_(n to oo) "det". (M_(n))=lambda-e^(-1)`. Find `lambda`.

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