Yes, you understand that despite Champagne and advanced years, you can't really compete. That must seem like a problem but just accept that you aren't here to compete but to learn. All will be well. Exponential series can be elusive. At first they seem cool but take your eye off them and they get out of hand. Then the fish really jump out of the basket.
Exponential series normally refers to 𝟏+𝔁/𝟏!+𝔁²/𝟐!+𝔁³/𝟑!+ … and I always thought it was very well behaved. You're a little skimpy on the details of how this relates to OP's question. Perhaps if you elaborated it would make it clearer.
I think you may have failed to fully take into account the formula 𝐎𝐩ₜ(𝒊ₘ) = 𝝅.>>
Broadly, an exponential series is any series that increases (or decreases) exponentially. It ought to be obvious (but it obviously isn't) that the possible variations of moves in a game of chess form such a series.
Don't worry about it.
If by "the possible variations of moves in a game of chess" you mean the number of different legal games of length 𝓷 ply (let's call it 𝓰ₙ) then you're right that it obviously isn't obvious to me that 𝓰ₙ is an exponential series. In fact it's obvious to me that it isn't.
In an exponential series 𝓰₁,𝓰₂,…𝓰ₙ,…, 𝓰ₖ₊₁/𝓰ₖ must be constant. By inspection 𝓰₁=𝟸𝟶, 𝓰₂=𝟸𝟶² but 𝓰₃ >𝟸𝟶³. The series is therefore not exponential.
That applies whether or not the 75 move rule is in force. If the 75 move rule is in force then it's also obvious that 𝓰ₙ=𝟶 whenever 𝓷>2.75(16.5+30)=16,500.
But mainly you still haven't explained what this has to do with OP's question.
I do not understand how anyone cannot realize that there have been more and more draws in World Championship matches? [just as I predicted]