Exercise 17, § 7 General Topology, IV, 400 If umn=1/(m2−n2)u_{mn} = 1/(m^2 - n^2)umn=1/(m2−n2) for m≠nm \neq nm=n and umm=0u_{mm} = 0umm=0, show that ∑m=1∞(∑n=1∞umn)=−∑n=1∞(∑m=1∞umn)≠0. \sum_{m=1}^{\infty} \left( \sum_{n=1}^{\infty} u_{mn} \right) = - \sum_{n=1}^{\infty} \left( \sum_{m=1}^{\infty} u_{mn} \right) \neq 0. m=1∑∞(n=1∑∞umn)=−n=1∑∞(m=1∑∞umn)=0. (Use Exercise 8.) Solution No solution has been written yet.