Why it works
A relaxed tone makes the sender feel less like a corporate robot and more like a peer. This lowers the reader's defensive walls because people tend to be more open to conversation with someone who feels like a friend.
Example
Hey, I was just reading your latest post on LinkedIn and wondered if you'd be open to chatting.
An illustration of the mechanism, not a template. Copied verbatim it stops being persuasion and starts being the pattern everyone else is already sending.
Is your sequence pulling this one?
Paste it in and find out which levers are working, which are missing, and which single zero is capping the whole message.