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    how would I go about this? thanks
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    (Original post by Maths&physics)
    how would I go about this? thanks
    Prove the base case, assume it's true for all n \leq k, prove it's true for n=k+1
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    (Original post by RDKGames)
    Prove the base case, assume it's true for all n \leq k, prove it's true for n=k+1
    I did n = 1 but im stuck.

    I assumed true for n = k and put into the equation both sides:

     6 U_k - 5 =  5 X 6^k^-^1 + 1

    then, k + 1:

     6 U_k_+_1 - 5 =  5 X 6^k + 1
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    (Original post by Maths&physics)
    I did n = 1 but im stuck.

    I assumed true for n = k and put into the equation both:

     6 U_k - 5 =  5 X 6^k^-^1 + 1

    then, k + 1:

     6 U_k_+_1 - 5 =  5 X 6^k + 1
    EDIT: Having looked at yours for a second glance, not sure what you're doing actually. Make your logical steps clearer!

    Assuming true for n=k means that we have u_k = 5\cdot 6^{k-1}+1.

    Substitute this into u_{k+1} = 6u_k-5 and rearrange to show that u_{k+1} = 5 \cdot 6^k +1
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    (Original post by RDKGames)
    EDIT: Having looked at yours for a second glance, not sure what you're doing actually. Make your logical steps clearer!

    Assuming true for n=k means that we have u_k = 5\cdot 6^{k-1}+1.

    Substitute this into u_{k+1} = 6u_k-5 and rearrange to show that u_{k+1} = 5 \cdot 6^k +1
    ok, initially assumed true for n = k for both?

    giving us:  6u_k-5 and u_k = 5\cdot 6^{k-1}+1.

    am I right?
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    (Original post by Maths&physics)
    ok, initially assumed true for n = k for both?

    giving us:  6u_k-5 and u_k = 5\cdot 6^{k-1}+1.

    am I right?
    Why for both? You only need to assume it for the statement you're trying to prove is true. The first one is always true since that's what the sequence is defined by.

    Anyway, as I said in my last post, sub your assumption into the first one and get the result.
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    (Original post by RDKGames)
    Why for both? You only need to assume it for the statement you're trying to prove is true. The first one is always true since that's what the sequence is defined by.

    Anyway, as I said in my last post, sub your assumption into the first one and get the result.



    firstly, we need to prove the series is true and leads us to: u_n = 5\cdot 6^{n-1}+1.

    so, the series: u_{n+1} = 6U_n - 5.

    assume true for n = k

    sub into series: u_{k+1} = 6U_k - 5

    then, n = k +1 into what it leads to?
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    (Original post by Maths&physics)
    firstly, we need to prove the series is true and leads us to: u_n = 5\cdot 6^{n-1}+1.

    so, the series: u_{n+1} = 6U_n - 5.

    assume true for n = k

    sub into series: u_{k+1} = 6U_k - 5

    then, n = k +1 into the series?
    No...

    It's actually a sequence, not a series like the question claims. They are two different things.

    The sequence is iteratively defined by u_{n+1} = 6u_n-5 ... (1)

    We are told to prove that the nth term is given by u_n = 5\cdot 6^{n-1} +1

    Testing for n=1 we find it's true. Assuming true for n \leq k we get that u_k = 5\cdot 6^{k-1}+1 ... (2)

    Now we wish to show that u_{k+1} = 5 \cdot 6^k +1.

    How? Well we know the kth term in terms of k, so we just need to use it to get the (k+1)th term in terms of k through the iterative formula (1).

    So, sub (2) into (1) and show the required result.
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    (Original post by Maths&physics)
    how would I go about this? thanks
    Where did you find this question?
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    (Original post by Msnotorious)
    Where did you find this question?
    the past papers.
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    (Original post by RDKGames)
    No...

    It's actually a sequence, not a series like the question claims. They are two different things.

    The sequence is iteratively defined by u_{n+1} = 6u_n-5 ... (1)

    We are told to prove that the nth term is given by u_n = 5\cdot 6^{n-1} +1

    Testing for n=1 we find it's true. Assuming true for n \leq k we get that u_k = 5\cdot 6^{k-1}+1 ... (2)

    Now we wish to show that u_{k+1} = 5 \cdot 6^k +1.

    How? Well we know the kth term in terms of k, so we just need to use it to get the (k+1)th term in terms of k through the iterative formula (1).

    So, sub (2) into (1) and show the required result.
    thanks
 
 
 
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