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I have the self-referencing recurrence relation $$ d(0) = 0 $$ $$ d(1) = a $$ $$ d(n+1) = d(n) + a*e^{-(\frac{d(n)-n*c}{b})^4} $$ Written as a sum: $$ d(N) = a*\sum_{n=0}^{N}e^{-(\frac{d(n)-n*c}{b})^...

In a problem that I'm working on currently, the following question came up and I feel this should be fairly elementary, but I couldn't prove it myself/couldn't find a reference. Any pointers or ...