feat(Add FastAPI + Vercel deployment option): (#4520)

# Update deployments doc with langcorn API server

API server example 

```python
from fastapi import FastAPI

from langcorn import create_service

app: FastAPI = create_service(
    "examples.ex1:chain",
    "examples.ex2:chain",
    "examples.ex3:chain",
    "examples.ex4:sequential_chain",
    "examples.ex5:conversation",
    "examples.ex6:conversation_with_summary",
)

```
More examples: https://github.com/msoedov/langcorn/tree/main/examples

Co-authored-by: Dev 2049 <dev.dev2049@gmail.com>

docs/additional_resources/deployments.md

@@ -29,6 +29,10 @@ It implements a Question Answering app and contains instructions for deploying t
 
 A minimal example on how to run LangChain on Vercel using Flask.
 
+## [FastAPI + Vercel](https://github.com/msoedov/langcorn)
+
+A minimal example on how to run LangChain on Vercel using FastAPI and LangCorn/Uvicorn.
+
 ## [Kinsta](https://github.com/kinsta/hello-world-langchain)
 
 A minimal example on how to deploy LangChain to [Kinsta](https://kinsta.com) using Flask.