Chapter 4.1, Problem 15E

Let V be the space of all infinite sequences of real numbers. See Example 5. Which of the subsets of V given in Exercises 12 through 15 are subspaces of V?

15. The square-summable sequences $\left(x_0,x_1,\mathrm{...}\right)$ (i.e., those for which ${\displaystyle \underset{i=0}{\overset{\infty }{\sum }}{x}_i^2}$ converges)