According to Medication Statement Resource it can use prescribed duration using effective period. Howevever in my case i want to set my end date to infinity or something like that (Given that doctor has prescribed some medications for entire lifespan). Is there any approach to achieve this scenario?
or is it conventional to use something like 'infinity' for end date?
Not sure there's a convention for that. There aren't a lot of countries where something like that would be allowed for a prescription. Typically you need to authorize either a quantity or a days supply. For MedicationStatement which just reflects a summary of what the patient is on, anything they're expected to take on an ongoing basis would have a start date but no end date for the period.
I'd encourage you to raise your use-case on chat.fhir.org where it can be discussed by the relevant people from the pharmacy work group and they can recommend the best solution for MedicationRequest.