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Think I have parts 1 and 2, struggling with the induction :S Any help greatly appreciated!
I think that the base case should be
Have a look at this webpage.
There is no need for induction on this question when you can prove it simply by re-writing the inequality but very well...
I am going to assume there was a misprint and they omitted that the result holds true for .
OP, from your induction hypothesis, you have for and you wish to show with the assumption that .
Now, recall that .
Multiply the inequality through by and the result falls out fairly quickly with some manipulation.
@Plato, I think you mean for as equality holds for .
No problem. There's nothing wrong with your working, you just need to do a bit of deduction for the last bit.
Clearly for
Also, this may be pedantic but I think you could make it a bit clearer that what you've done is that you've taken your inductive assumption and you've multiplied that through by and then added 1.
It's not beyond you, just keep going at it! Practice makes pefect.
Clearly if .
Substitute for and then you have the rightmost inequality in my above post. You will be able to simplify that down into a fraction, call it . The denominator of will clearly be and so clearly iff the numerator of . Try it, you'll be able to sneak in the result from part C.
Also, I see you're a fellow Scot! Are you studying Mathematics @ Glasgow?