Is it valid to write check without numeric amount but with words amount?

Is it valid to write check without numeric amount but with words amount?

It appears so. From from the accepted answer to the exact opposite question:

The Uniform Commercial Code section 3 covers negotiable instruments.

§ 3-114. CONTRADICTORY TERMS OF INSTRUMENT

If an instrument contains contradictory terms, typewritten terms prevail over printed terms, handwritten terms prevail over both, and words prevail over numbers.

To your other question:

Will my check get cashed in this way ?

It should, but the teller might not know the law, or the bank might have a policy to reject such checks.

To be safe, I'd contact the people you wrote the check to.