A new series is formed by taking two positive terms of the alternating harmonic…
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
A new series is formed by taking two positive terms of the alternating harmonic series for every one negative term, in the order:
1+31−21+51+71−41+91+111−61+⋯
What happens to this rearranged series?
(a) It converges and still sums to ln2.
(b) It converges, but to a value greater than ln2.
(c) It diverges to +∞.
(d) It diverges by oscillating between two finite bounds.