Show 1/(n+1)+1/(n+2)+1/(n+3)+1/2n>3/5, for n>2. Use mathematical induction.

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- March 2nd 2010, 04:52 PMGamesonPlanesInduction Proof (Inequality) SIMPLE!!
Show 1/(n+1)+1/(n+2)+1/(n+3)+1/2n>3/5, for n>2. Use mathematical induction.

THANKS - March 2nd 2010, 05:13 PMArchie Meade
- March 3rd 2010, 02:38 AMemakarov
I think the statement is correct. To prove it by induction, write the nth and (n+1)st sums: ; . Then express as where is some expression of n, i.e., . If you show that , you are done.

Note that has three terms, and two of them are at least as big as half of the third. - March 3rd 2010, 02:58 AMArchie Meade