#can someone help correct my method

28 messages · Page 1 of 1 (latest)

drowsy vergeBOT
#
  1. Do not ping the Moderators, unless someone is breaking the rules.
  2. Do not ping the Helper Moderators, unless there is a conflict between helpers.
  3. Do not ping other members randomly for help.
  4. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
  5. Wait patiently for a helper to come along.
  6. If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:

ebon dagger
shut crown
#

what do you think?

ebon dagger
#

idk what i did wrong

shut crown
#

ah, okay.

keen inlet
shut crown
#

$\frac{1}{3}n(2n+1)(2n-1)+2n(n+1)(2n+1)$

granite stormBOT
#

flying green people eater

1245133657690214403.png
shut crown
#

the conversion from this step to the next is wrong

keen inlet
#

the sum of the two parts is not S_n but S_2n

shut crown
#

o

keen inlet
#

Here's why

shut crown
#

i think brain is freid

keen inlet
#

$S_{2n} = \sum_{k=1}^{2n} (2 + (-1)^k)k^2$

granite stormBOT
keen inlet
#

From here, you reformulate this sum by grouping the terms 2r and 2r-1 together

#

$S_{2n} = \sum_{r=1}^{n} \left((2r-1)^2 + 3(2r)^2\right) = \left(\sum_{r=1}^{n} (2r-1)^2\right) + \left( \sum_{r=1}^{n} 3(2r)^2 \right)$

granite stormBOT
keen inlet
#

which is exactly what you already computed

#

this is the only thing you need to fix

ebon dagger
keen inlet