What is a statement that is true for any number or variable?
2 answers:
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If 
is an integer, you can use induction. First show the inequality holds for 
. You have 
, which is true.
Now assume this holds in general for
, i.e. that 
. We want to prove the statement then must hold for 
.
Because, you have
and this must be greater than
for the statement to be true, so we require
for
. Well this is obviously true, because solving the inequality gives 
. So you're done.
If you is any real number, you can use derivatives to show that 
increases monotonically and faster than .
Now assume this holds in general for
Because
and this must be greater than
for
If you
The graph of the sequence M , we define M recursively using function notation
Given :
the graph of the sequence M
Lets write the recursive function using the given points
First point is (1,7) and second point is (2,5) then (3,3) and so on
For recursive function , we use the initial point (1,7)
when n=1, f(n)=7
the y values of the point are decreasing by 2. Common difference is -2
Recursive function is
where n=2,3,4...
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