i'm reading shilov's "real and complex analysis". there is a problem to prove that for real positive x1,x2,...xn, if x1*x2*...*xn=1, then x1+x2+...xn >= n. I proved this for the case n = 2. it says use induction on this case to prove it for the nth case. but i just don't see it.(adsbygoogle = window.adsbygoogle || []).push({});

for n=2:

(a+1)^2 >= 0

a^2 + 2a + 1 >= 0

a^2 + 1 >= 2a

a + 1/a >= 2

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

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

# If the product of n numbers is 1, their sum is >= n

Loading...

Similar Threads - product numbers | Date |
---|---|

B Product rule OR Partial differentiation | Jan 10, 2018 |

B Derivative with the double cross product | Jul 18, 2017 |

B Derivation with logarithms and product | May 27, 2017 |

I Geometrical interpretation of gradient | May 26, 2017 |

Deriving functions relating to condition numbers | Mar 23, 2017 |

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