Why does the value of a converging alternating scries lie

Problem 3EWhy does the value of a converging alternating series lie between any two consecutive terms of its sequence of partial sumsSolutionStep 1 of 2In this problem we need to find why does the value of a converging alternating series lie between any two consecutive terms of its sequence of partial sums.Consider the general alternating series. for which for ,such that the terms are non-increasing in magnitude: for Now specifically, consider the sequence of even-numbered partial sums:Because , each quantity in parentheses is a non-negative number, which means for n 0. That is, the sequence of even-numbered partial sums is bounded below. A similar grouping of terms can be used to show that for n 0, so this sequence is also bounded above.