Given a sequence f: z+→r of real numbers, we say that the sequence converges to a real number l if for all ε> 0, there exists a positive integer n such that for any positive integer n, if n≥n, then |f(n)-l|< ε. prove that if a sequence f converges to l and a sequence g converges to m, then the sequence f+g converges to l+m. (you may use the triangle inequality: |a+b|≤|a|+|b| for any real numbers a and b.)

The height of a birch tree, f(x), in inches, after x months is shown in the graph below. how much does the birch tree grow per month, and what will be the height of the birch tree after 10 months? a. the birch tree grows 1 inch per month. the height of the birch tree will be 16 inches after 10 months. b. the birch tree grows 2 inches per month. the height of the birch tree will be 26 inches after 10 months. c. the birch tree grows 3 inches per month. the height of the birch tree will be 36 inches after 10 months. d. the birch tree grows 2 inches per month. the height of the birch tree will be 24 inches after 10 months.