"Suppose (a_n) is a bounded increasing seq and (b_n) is a bounded decreasing seq. Let x_n=a_n+b_n. Show that converges."

Triangle ineq yields

from which point I am unable to deduce that either of the RHS sums converge.

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- Mar 10th 2006, 10:00 AMTreadstone 71Series
"Suppose (a_n) is a bounded increasing seq and (b_n) is a bounded decreasing seq. Let x_n=a_n+b_n. Show that converges."

Triangle ineq yields

from which point I am unable to deduce that either of the RHS sums converge. - Mar 10th 2006, 10:36 AMTreadstone 71
Got it, thanks.