wampominater
  • wampominater
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
Mathematics
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SOLVED
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chestercat
  • chestercat
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wampominater
  • wampominater
\[4\times6 + 5 \times7 +6\times8 +... + 4n(4n+2) = \frac{ 4(4n+1)(8n+7) }{ 6 }\]
freckles
  • freckles
well first step is try to show it is true for n=1
wampominater
  • wampominater
is n = 1 4? or 4x6

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freckles
  • freckles
for n=1 you only have one term which is the 4*6 on the left hand side
wampominater
  • wampominater
ok so I am trying to show that 24 = the fraction at the end there
freckles
  • freckles
yes for n=1
wampominater
  • wampominater
ok, and if that doesnt = 24 then it is false, right?
freckles
  • freckles
right
wampominater
  • wampominater
alright, I just didnt know if i was doing it right, Thank you for the help, I think thats all I need.
freckles
  • freckles
np
freckles
  • freckles
if the left side confuses you I can show you what the left side looks like for n=2
freckles
  • freckles
or even n=3
wampominater
  • wampominater
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 +
freckles
  • freckles
ok cool stuff
wampominater
  • wampominater
thanks for the help! :)

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