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Bug introduced in 10.0 and persisting through 11.0  (reported as CASE:3790525)

Here's a simple series:

Sum[t^k DiscreteDelta[k]/k!,{k,0,Infinity}] 

Mathematica says that it doesn't converge. But replacing Infinity by any positive integer I get 1. The same is for the case when I remove k! or t^k from the expression.

What's going on? Shouldn't k! improve convergence rather than lead to divergence?

Note also that Mathematica can solve this easily:

Sum[f[k] DiscreteDelta[k], {k, 0, Infinity}] (* f[0] *) 

Bug introduced in 10.0 and fixed in 11.1 
(reported as CASE:3790525)

Here's a simple series:

Sum[t^k DiscreteDelta[k]/k!,{k,0,Infinity}] 

Mathematica says that it doesn't converge. But replacing Infinity by any positive integer I get 1. The same is for the case when I remove k! or t^k from the expression.

What's going on? Shouldn't k! improve convergence rather than lead to divergence?

Note also that Mathematica can solve this easily:

Sum[f[k] DiscreteDelta[k], {k, 0, Infinity}] (* f[0] *) 

Bug introduced in 10.0 and persisting through 11.0

Here's a simple series:

Sum[t^k DiscreteDelta[k]/k!,{k,0,Infinity}] 

Mathematica says that it doesn't converge. But replacing Infinity by any positive integer I get 1. The same is for the case when I remove k! or t^k from the expression.

What's going on? Shouldn't k! improve convergence rather than lead to divergence?

Note also that Mathematica can solve this easily:

Sum[f[k] DiscreteDelta[k], {k, 0, Infinity}] (* f[0] *) 

Bug introduced in 10.0 and persisting through 11.0 (reported as CASE:3790525)

Here's a simple series:

Sum[t^k DiscreteDelta[k]/k!,{k,0,Infinity}] 

Mathematica says that it doesn't converge. But replacing Infinity by any positive integer I get 1. The same is for the case when I remove k! or t^k from the expression.

What's going on? Shouldn't k! improve convergence rather than lead to divergence?

Note also that Mathematica can solve this easily:

Sum[f[k] DiscreteDelta[k], {k, 0, Infinity}] (* f[0] *) 

Here's a simple series:

Sum[t^k DiscreteDelta[k]/k!,{k,0,Infinity}] 

Mathematica says that it doesn't converge. But replacing Infinity by any positive integer I get 1. The same is for the case when I remove k! or t^k from the expression.

What's going on? Shouldn't k! improve convergence rather than lead to divergence?

Note also that Mathematica can solve this easily:

Sum[f[k] DiscreteDelta[k], {k, 0, Infinity}] (* f[0] *) 

Bug introduced in 10.0 and persisting through 11.0

Here's a simple series:

Sum[t^k DiscreteDelta[k]/k!,{k,0,Infinity}] 

Mathematica says that it doesn't converge. But replacing Infinity by any positive integer I get 1. The same is for the case when I remove k! or t^k from the expression.

What's going on? Shouldn't k! improve convergence rather than lead to divergence?

Note also that Mathematica can solve this easily:

Sum[f[k] DiscreteDelta[k], {k, 0, Infinity}] (* f[0] *)