SOLUTION: I'm sorry for asking this again but the way I typed this up the last time was quite confusing.
Use mathematical induction to prove that the following is true for every positive
Algebra ->
Sequences-and-series
-> SOLUTION: I'm sorry for asking this again but the way I typed this up the last time was quite confusing.
Use mathematical induction to prove that the following is true for every positive
Log On
Question 987057: I'm sorry for asking this again but the way I typed this up the last time was quite confusing.
Use mathematical induction to prove that the following is true for every positive integer n:
1/4+2*1/4+4*1/4+...+[2(n-1)+1/4]=4n^2-3n/4
Thank you for your help. Answer by Edwin McCravy(20056) (Show Source):
But the 2nd and 3rd terms are still wrong!
They must be what you get when you substitute n=2 and n=3 into
the general term [2(n-1)+1/4]
But watch what happens when you substitute n=2 into [2(n-1)+1/4]
You get
[2(2-1)+1/4] = [2(1)+1/4] = [2+1/4] = [8/4+1/4] = 9/4 and 9/4 is NOT 2*1/4
See?
Also watch what happens when you substitute n=3 into [2(n-1)+1/4]
You get
[2(3-1)+1/4] = [2(2)+1/4] = [4+1/4] = [16/4+1/4] = 17/4 and 17/4 is NOT 4*1/4.
The sequence is botched. The induction proof I gave you is correct.
Edwin
