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We prove a kind of bilateral semi-terminating series related toRamanujan-like series for negative powers of $\pi$, and conjecture a type ofsupercongruences associated to them. We support this conjecture by checking allthe cases for many primes. In addition we are able to prove a few of them fromsome terminating hypergeometric identities. Finally, we make an intriguingobservation.

Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences