Tutors Answer Your Questions about Equations (FREE)
Question 7468: I am trying to prove the following identity by induction (basic number theory course):
1^2 + 2^2 + ... + k^2 = (n*(n+1)*(2*n + 1))/6
So far I have that when n = 1, LHS = 1^2, RHS = (1*2*3)/6 = 6/6 = 1
therefore the theory is true when n = 1
Assume it is true for some positive integer k
1^2 + 2^2 + ... + k^2 = (k*(k+1)*((2*k)+1))/6
then try to prove it is also true for k+1
1^2 + 2^2 + ... + k^2 + (k+1)^2 = ((k*(k+1)*((2*k)+1))/6) + (k+1)^2
I can rearrange this to give me (1/6*(k+1)* k*((2*k)+1)) + (k+1)^2
and I can factor (k+1)^2 to give me k^2 + 2k + 1 but I'm not sure I'm making any progress.
I found a solution that shows the next step is
(1/6*(k+1) * (k*((2*k)+1) + (6*(k+1)))
but I can't figure how to get there from where I am.
Any help would be greatly appreciated.
Click here to see answer by longjonsilver(2297)   |
Question 8188: I am reviewing for a math placement test and have not taken any math courses in 3 years. The following are sample problems I was provided with that are meant to be representative of test problems. I have the answers, but if you could show me step by step how to solve them and any general guidelines you have for these types of problems, it would be greatly appreciated.
Solve these equations for x:
1.  2.  3. 
4. 
Thank you, Ashley
Click here to see answer by Earlsdon(4898)  |
Question 8371: what is -3 + 2b =-9
Add 3 to both sides:
3 + -3 +2b = -9 + 3
That cancels the 3's on the one side and you get 2b by itself.
2b = -9 + 3
2b = -6
Divide both sides by 2, so you can have the b by itself
2b/2 = -6/2
b = -3
Click here to see answer by elima(1433) |
Question 8475: The world's fastest regular steam train, the Cheltenham Flyer, once traveled 77.3 miles at an average spped of 81.8 miles per hour. How long did the trip take? I know the equation is D=rt but I'm not sure of answer
Click here to see answer by srinivas123(23) |
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