Find Signal x(n) - Hint for Solving x(n)+x(-n)

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To solve the equation x(n) + x(-n) where x(n) = n*v(n-1), it is essential to recognize that x(n) is a vector function defined for all integers. The term nv(n-1) indicates that each element of the vector v(n) is multiplied by its corresponding integer n, with v(n-1) representing a rightward shift of the vector v(n). The challenge lies in determining the properties of the resulting signal when combining x(n) and x(-n). Understanding the symmetry and behavior of the signal will aid in finding the solution. A clear grasp of vector manipulation and signal properties is crucial for progressing with the problem.
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I have to find the signal if x(n) = nv(n-1) for -infinite < n < + infinite

x(n)+x(-n)

Can I get hint with this problem so I can do rest of them. Thanks
 
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x(n) is a vector function where n is all the intergers from -infinity to +infinity. nv(n-1) is n*v(n-1) which is the multiplication of two vectors. Again n is all integers from -infinity to +infinity and v(n-1) is the vector function v(n) after all the elements have been shifted over one position to the right.

At least that's what it looks like form my position.
 
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