For $i\in \mathbb{N}$, define $L_i :=${$ ⟨M⟩ |$ On input $101$ M halts after at most i steps}
For any fixed i the language $L_i$ is decidable as if there is no end state up to the i$^{th}$ position on the tape of the turing machine then $L$ doesn't terminate.
However i have been asked to Use Rice’s theorem to prove that $L = \cup$ $L_i$ with $i \in \mathbb{N}$ is undecidable.
How would i do this? could I compose the tapes and which would never halt as it would be the sum of the natural numbers?
thanks for the help in advance.