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Complex Algebra & Analysis Help watch

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    Hi guys.

    A little stuck on the following question. Wondering if anybody could help out and solve it.

    Thanks

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    (Original post by sj1996)
    Hi guys.

    A little stuck on the following question. Wondering if anybody could help out and solve it.

    Thanks

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Views: 63
Size:  75.7 KB
    Well for the first part you just need to write down the inequality

    a_n \leq a_{n+1}

    in terms of n and rearrange using standard methods. That shouldn't be too difficult.

    Bernoulli's inequality states that

    (1+x)^r \geq 1+rx

    for certain x and r (but those conditions aren't an issue because n is presumably positive).

    So here's a hint:

    n(n+2) = n^2 + 2n = (n+1)^2 -1

    Now have a go at it and let us know if you need further help
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    (Original post by Indeterminate)
    Well for the first part you just need to write down the inequality

    a_n \leq a_{n+1}

    in terms of n and rearrange using standard methods. That shouldn't be too difficult.

    Bernoulli's inequality states that

    (1+x)^r \geq 1+rx

    for certain x and r (but those conditions aren't an issue because n is presumably positive).

    So here's a hint:

    n(n+2) = n^2 + 2n = (n+1)^2 -1

    Now have a go at it and let us know if you need further help
    Thank you. I was wondering if you could help out with the rearrangement because I've tried so many times and still can't get a result! Thanks
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    (Original post by sj1996)
    Thank you. I was wondering if you could help out with the rearrangement because I've tried so many times and still can't get a result! Thanks
    Try multiplying both sides by

    \left(1-\dfrac{1}{n+1}\right)^{n+1}

    and then simplify the LHS
 
 
 
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