mathematical induction

[jfsfroggy]

Use mathematical induction to prove that the statement is true for ever positive integer n.

9 + 2*9 + 3*9 + ... + 9n=9n(n+1)/2

So far I have:

Show Ssub1 true
S sub1 = 1
S sub1 = 9(1)(1+1)/2
9(1) = 9(2)/2
9=9

Assume S subk = 9k(k+1)/2 is true
We must show S subk+1 = 9(k+1)(k+2)/2

Iam lost after this step, can someone please help me out?

Thanks,
Jessica

 

[Unco]

It helps to write the induction assumption out in full, Jessica:

"Assume: 9 + 2*9 + 3*9 + ... + 9k = 9k(k+1)/2"

Then all that is left to do is to use this assumption with S(k+1):

LHS = 9 + 2*9 + 3*9 + ... + 9k + 9(k+1) = ? + 9(k+1)

and show this equals the desired right-hand side (RHS).

 

[tkhunny]

Assume S subk = 9k(k+1)/2 is true
We must show S subk+1 = 9(k+1)(k+2)/2

You're on the right track. Notice that S_k+1 = S_k + 9*(k+1)

 

[jfsfroggy]

so, am i correct in assuming...

9(k+1)(k+2)/2=9k(k+1)/2+9(k+1) ?

 

[tkhunny]

No, that's what you are trying to demonstrate. All you need is algebra.