SOLUTION: use mathematical induction to prove the summation of  i=1 4i-1=n(2n+1)

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Question 935544: use mathematical induction to prove the summation of 
i=1
4i-1=n(2n+1)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You probably meant
sum%28%284i-1%29%2C+i=1%2C+i=n+%29=n%282n%2B1%29

For n=1 , what we need to prove is
sum%28%284i-1%29%2C+i=1%2C+i=1+%29=1%282%2A1%2B1%29
sum%28%284i-1%29%2C+i=1%2C+i=1+%29=4%2A1-1=4-1=3 is the "sum" of just the first term, 3 .
1%282%2A1%2B1%29=1%282%2B1%29=1%2A3=3 has the same value.

After that we have to prove that
if sum%28%284i-1%29%2C+i=1%2C+i=n+%29=n%282n%2B1%29 is true for n=k ,
it must be true for n=k%2B1 .
For n=k ,
we say it is true that sum%28%284i-1%29%2C+i=1%2C+i=n+%29=n%282n%2B1%29 , so
sum%28%284i-1%29%2C+i=1%2C+i=k+%29=k%282k%2B1%29 .
Then, we must prove that it is true for n=k%2B1 , meaning that