Hello, I have a question i can figure out.(adsbygoogle = window.adsbygoogle || []).push({});

THE QUESTION:

Show that

[tex]\sqrt{2}, \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}, ...[/tex]

converges and find the limit.

From what I see, the first term is root 2, the second term will be the root of 2 times the first term making it larger than the first term, the third term will be the root of 2 times the second term making it larger than the second term.

How can this converge to a real number?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Convergent Series Question

Loading...

Similar Threads - Convergent Series Question | Date |
---|---|

Question on fourier series convergence | Mar 28, 2014 |

Question about radius of convergence of fractional power series | Dec 4, 2011 |

Extremely simple question regarding the convergence of a series | Nov 10, 2011 |

Question about series convergence/divergence | Nov 22, 2008 |

Infinitie Series: Converge/Diverge question | Mar 28, 2005 |

**Physics Forums - The Fusion of Science and Community**