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Putnam 2016 B1

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December 4, 2016
PutnamPutnam 2016Putnam calculus

Problem Statement

Let x0,x1,x2,…x_0,x_1,x_2,\dots be the sequence such that x0=1x_0=1 and for n≥0,n\ge 0, xn+1=ln⁡(exn−xn)x_{n+1}=\ln(e^{x_n}-x_n) (as usual, the function ln⁡\ln is the natural logarithm). Show that the infinite series x0+x1+x2+⋯x_0+x_1+x_2+\cdots converges and find its sum.
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