Hi
(note that )
(note that )
(note that )
Can you guess what has to be shown ?
Q: Given that f(n) = (1/2!) + (2/3!) + 3/4!) +...+ [n/(n+1)!], where n is a positve integer, find the values of f(1), f(2) and f(3). hence make a conjecture for a forumla for f(n) in terms of n and prove it using mathematical induction.
Thank you in advance!
Hello, Tangera!
This is quite a task . . .
Given that: . .where is a positve integer.
(a) Find the values of
(b) Make a conjecture for a formula for in terms of
(c) Prove it using mathematical induction.
(b) The denominator seems to be:
. . .The numerator seems to be "one less":
The function seems to be: .
Verify . . . True
Assume
Add to both sides:
. .
The left side is the left side of
We must show that the right side is the right side of
The right side is: .
. . . . . There!
The inductive proof is complete.