SOLUTION: Show, by the Principle of Mathematical Induction: 8 + 16 + 24+…+8n = 4n(n+1) for n≥1

Algebra ->  Probability-and-statistics -> SOLUTION: Show, by the Principle of Mathematical Induction: 8 + 16 + 24+…+8n = 4n(n+1) for n≥1       Log On


   

Question 1102037: Show, by the Principle of Mathematical Induction:
8 + 16 + 24+…+8n = 4n(n+1) for n≥1
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Show, by the Principle of Mathematical Induction:
8 + 16 + 24+…+8n = 4n(n+1) for n≥1
-----
Show it is true for n = 1
8 = 4(2)
-------------------
Assume it is true for n = k
8 + 2*8 + 3*8 + ... + 8k = 4k(k+1)
------------------------
Show that it must be true for n = k+1
8 + 2*8 + 3*8 + ... + 8k + (k+1)8 = 4(k+1)(k+2)
------
Note:: The 1st 8 terms = 4k(k+1) so you get::
4k(k+1) + (k+1)(8) = (k+1)[4k+8] = (k+1)*4(k+2) = 4(k+1)(k+2)
----------------
Cheers,
Stan H.
------------