Need help to solve a summation till infinity problem

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I need to solve a problem in SageMath:

P = sum of alpha_m from (K-1) till infinity,

where

alpha_m = integrate((((lmd*t)^m)/factorial(m))*b(t)*exp(-lmd*t), t,0,infinity),

and lmd is a constant value.

How to feed this in SageMath? I tried to input as:

sum((integrate((((lmd*t)^m)/factorial(m))*b(t)*exp(-lmd*t), t,0,infinity)), m,K-1,infinity)

It shows error.