Hello!
I think that the root sign acts on entire fractions, i.e. we have the sequence
`sqrt(5/4),` `sqrt(3/2),` `sqrt(7/4).`
Let's express the second fraction as `6/4` and the sequence becomes
`sqrt(5/4), sqrt(6/4), sqrt(7/4).`
Now the rule is obvious: n-th term is `sqrt((n+4)/4)` if we start from `n=1.` This is the same as `sqrt(1+n/4).`
That said, there are infinitely many possible formulas for these three numbers, even among polynomial formulas.
Hello!
I think that the root sign acts on entire fractions, i.e. we have the sequence
`sqrt(5/4),` `sqrt(3/2),` `sqrt(7/4).`
Let's express the second fraction as `6/4` and the sequence becomes
`sqrt(5/4), sqrt(6/4), sqrt(7/4).`
Now the rule is obvious: n-th term is `sqrt((n+4)/4)` if we start from `n=1.` This is the same as `sqrt(1+n/4).`
That said, there are infinitely many possible formulas for these three numbers, even among polynomial formulas.
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