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wampominater

  • one year ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.

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  1. wampominater
    • one year ago
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    \[4\times6 + 5 \times7 +6\times8 +... + 4n(4n+2) = \frac{ 4(4n+1)(8n+7) }{ 6 }\]

  2. freckles
    • one year ago
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    well first step is try to show it is true for n=1

  3. wampominater
    • one year ago
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    is n = 1 4? or 4x6

  4. freckles
    • one year ago
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    for n=1 you only have one term which is the 4*6 on the left hand side

  5. wampominater
    • one year ago
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    ok so I am trying to show that 24 = the fraction at the end there

  6. freckles
    • one year ago
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    yes for n=1

  7. wampominater
    • one year ago
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    ok, and if that doesnt = 24 then it is false, right?

  8. freckles
    • one year ago
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    right

  9. wampominater
    • one year ago
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    alright, I just didnt know if i was doing it right, Thank you for the help, I think thats all I need.

  10. freckles
    • one year ago
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    np

  11. freckles
    • one year ago
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    if the left side confuses you I can show you what the left side looks like for n=2

  12. freckles
    • one year ago
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    or even n=3

  13. wampominater
    • one year ago
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    I think i get it now, it was confusing cause it was 4 x 6, but now i realize that since it is a sum that the terms are seperated by +

  14. freckles
    • one year ago
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    ok cool stuff

  15. wampominater
    • one year ago
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    thanks for the help! :)

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