How do I calculate this w/o brute forcing it, It isn't arithmetic nor geometric so how would I got about with calculating it?
#Summation of logarithmic function
agile mantle
severe oliveBOT
How do I calculate this w/o brute forcing it, It isn't arithmetic nor geometric ...
- Wait patiently for a helper to come along.
- Once someone helps you, say thank you and close the thread with:
+close
- Feel free to nominate the person for helper of the week in #helper-nominations
- Do not ping the mods, unless someone is breaking the rules.
- If you're happy with the help you got here, and the server overall, you can contribute financially as well:
agile mantle
I was trying to find a way to work with it with the log base change rule
but I cant really find a way
viscid parcel
@agile mantle
it works with the log base change rule
change it all to base 3
and it all cancels out beautifully
agile mantle
hold on let me write it out
does it have to be base 3 or can I use any base
I think im losing u lmao
oh wait I think I see what u mean
viscid parcel
change it to the base of the first logarithm so there isnt an annoying denominator
agile mantle
should be ln (n-1) / lnn
yeah lol
oh
ig I dont think itl matter though no?
itl still be log base 3 of 6 at the end no?
slate crescent
yeah, log3(n)
agile mantle
why not just keep it as ln just to make it simple at the beggining
wouldnt it make now difference
slate crescent
because look at what the sum is
f(3^k)
log base 3 of that is quite easy to find
agile mantle
oh I see waht u mean
what*
yeah ig
I mean we get calculators anyways but yeah thats true
agile mantle
and it all cancels out beautifully
also would for example f(4) only be log3(4) or would it move up 4 in the sequence, ie; log3(4) * log5(6) * log6(7) * log7(8)
im assuming the first option
ik its kind of a dumb question
@slate crescent
slate crescent
im assuming the first option
yes
slate crescent
yes
agile mantle
yes
also just to confirm, the way I solved it from there was just brute force it
just add up all 20 of them
after knowing the shortcut for f(n)
or u could just look at it as 1 + 2 +3 + 4 +5 +6 +7 +8 +9 +10.... all the way to 20 ig
slate crescent
it’s 3 + … + 20
agile mantle
mby eah
slate crescent
there is a shortcut
agile mantle
just realized when i started writing it out lol
u can just arithmetic sequenece it
.
common difference is 1
agile mantle
23*9
ima be honest idk how u got that 23*9
buti m just gonna stick with n = 18, u1 = 3
d = 1
then just sum it
nvm I jsut got the same thing
agile mantle
3 + 20 + 4 + 19 + 5 + 18
whyd u write this though lol
slate crescent
whyd u write this though lol
helps see that it’s adding 23 up
each takes 2 terms, there are 18 terms, so 9 23s
cursive prairie
agile mantle
+close