If A =
1 3
2 6
show that A^n= 7^n-1
1 3
2 6
Answers
Answer:
answer is 26
Step-by-step explanation:
I hope it will help you
Step-by-step explanation:
There is an extremely powerful tool in discrete mathematics used to manipulate sequences called the generating function. The idea is this: instead of an infinite sequence (for example:
2
,
3
,
5
,
8
,
12
,
…
) we look at a single function which encodes the sequence. But not a function which gives the
n
th term as output. Instead, a function whose power series (like from calculus) “displays” the terms of the sequence. So for example, we would look at the power series
2
+
3
x
+
5
x
2
+
8
x
3
+
12
x
4
+
⋯
which displays the sequence
2
,
3
,
5
,
8
,
12
,
…
as coefficients.
An infinite power series is simply an infinite sum of terms of the form
c
n
x
n
were
c
n
is some constant. So we might write a power series like this:
∞
∑
k
=
0
c
k
x
k
.
or expanded like this
c
0
+
c
1
x
+
c
2
x
2
+
c
3
x
3
+
c
4
x
4
+
c
5
x
5
+
⋯
.
When viewed in the context of generating functions, we call such a power series a generating series. The generating series generates the sequence
c
0
,
c
1
,
c
2
,
c
3
,
c
4
,
c
5
,
…
.
In other words, the sequence generated by a generating series is simply the sequence of coefficients of the infinite polynomial.