Prove that for each natural it's
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Use proof by induction (I): Let n=2 Then and on 1<x<2, , so the above integral is . (II): Assume that for n. Now, . Using the fact that for n<x<n+1 in the rightmost integral, And we have our proof. --Kevin C.
... i was about to give the same proof.. but i can't fix the latex.. haha
Okay! We have hence finally And we're done!
brilliant solution!!
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