Friday, August 30, 2013

√5/4,√3/2,√7/4. Find the formula for this sequence. √ this symbol means square root

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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