Letting (x) denote the fractional part of the real number x (see Exercise 16, Chap. 4 , for the definition), consider the function f(x)=∑n=1^∞ ((n x))/(n^2) (x real ) Find all discontinuities of f, and show that they form a countable dense set. Show that f is nevertheless Riemann-integrable on every bounded interval. | Numerade
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Letting (x) denote the fractional part of the real number x (see Exercise 16, Chap. 4 , for the definition), consider the function f(x)=∑n=1^∞ ((n x))/(n^2) (x real ) Find all discontinuities of f,
Letting (x) denote the fractional part of the real number x (see Exercise 16, Chap. 4 , for the definition), consider the function f(x)=∑n=1^∞ ((n x))/(n^2) (x real ) Find all discontinuities of f, and show that they form a countable dense set. Show that f is nevertheless Riemann-integrable on every bounded interval.
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