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Need help to solve a summation till infinity problem

I need to solve a problem in sagemath:

P = sum of alpha_m from (K-1) till infinity, where alpha_m = integrate((((lmdt)^m)/factorial(m))b(t)exp(-lmdt), t,0,infinity), lmd is a constant value.

How to feed this in sagemath. I tried to input as: sum((integrate((((lmdt)^m)/factorial(m))b(t)exp(-lmdt), t,0,infinity)), m,K-1,infinity).

It shows error.

Need help to solve a summation till infinity problem

I need to solve a problem in sagemath:SageMath:

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

where

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

and lmd is a constant value. value.

How to feed this in sagemath. SageMath? I tried to input as: sum((integrate((((lmdt)^m)/factorial(m))b(t)exp(-lmdt), as:

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

m,K-1,infinity)

It shows error.