Question

Use math notation to describe the following sequence: 1, -1, 1, -1,...

Answer 1

Answer:

The math notation to the given sequence is  $a_n=(-1)^{n+1}$ for n=1,2,3,... is verified and it is true

Step-by-step explanation:

Given sequence is 1,-1,1,-1,...

Let $a_1=-1,a_2=1,a_3=-1,a_4=-1,...$

To find the math notation for the given sequence :

$a_n=(-1)^{n+1}$ for n=1,2,3,... verify that it is true or not

Put n=1 in the above equation we get

$a_1=(-1)^{1+1}$

$=(-1)^2$

Therefore $a_1=1$

Put n=2 in the $a_n=(-1)^{n+1}$ equation we get

$a_2=(-1)^{2+1}$

$=(-1)^3$

Therefore $a_2=-1$

Put n=3 in the $a_n=(-1)^{n+1}$ equation we get

$a_3=(-1)^{3+1}$

$=(-1)^4$

Therefore $a_3=1$

and so on

Therefore the math notation to the given sequence is  $a_n=(-1)^{n+1}$ for n=1,2,3,... is verified and it is true