Hi, the question I have is:
a) Use mathematical induction to prove that
for n=1,2,3...
b) Deduce that
for n=1,2,3...
justify your answer.
For a) I have the following, so far:
Let p(n) be the variable proposition
For n=1, the sum is
The right hand side gives:
So p(1) is tue.
Assuming p(k) is true, I get:
next I tried to deduce that p(k+1) is true, that is:
Is this right so far?
Thanks for your help
Your Proposition P(k) is
Your Proposition P(k+1) is
If you can show that P(k+1) will be definately true if P(k) is true,
then you will have completed the inductive step.
We use
If P(k) is true, then we need to check if
The fraction 3/4 is irrelevant to comparing the LHS and RHS of the immediately above,
hence we want to know if
or
One way to check if the LHS equals the RHS is to multiply the 1st term of the LHS by
and multiply the 2nd term of the LHS by
and then multiply both sides (RHS and LHS) by
Then both sides will have a common denominator, so you only need compare numerators.
If you prefer, you could post the steps you've taken and we can check your work.