- #1
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I'm curious to answer (or at least reasonably understand) what the answer to:
[tex]\sqrt{a}+\sqrt{a+\sqrt{a}}+\sqrt{a+\sqrt{a+\sqrt{a}}}+...[/tex]
might be, where a>0.
It doesn't follow any ordinary pattern, such as an arithmetic or geometric progression. Also, if there is for any reason an easily derivable answer only for certain values of 'a', then that would also be interesting to hear.
edit: This problem diverges as hamster143 has noticed.
Instead, [tex]\sqrt{a}+\sqrt{a-\sqrt{a}}+\sqrt{a-\sqrt{a-\sqrt{a}}}+...[/tex] where a>1
[tex]\sqrt{a}+\sqrt{a+\sqrt{a}}+\sqrt{a+\sqrt{a+\sqrt{a}}}+...[/tex]
might be, where a>0.
It doesn't follow any ordinary pattern, such as an arithmetic or geometric progression. Also, if there is for any reason an easily derivable answer only for certain values of 'a', then that would also be interesting to hear.
edit: This problem diverges as hamster143 has noticed.
Instead, [tex]\sqrt{a}+\sqrt{a-\sqrt{a}}+\sqrt{a-\sqrt{a-\sqrt{a}}}+...[/tex] where a>1
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