Let be a real number

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let rr be a real number. For which values of rr does the alternating geometric series ∑n=0∞(−1)nr n\displaystyle\sum_{n=0}^{\infty} (-1)^n r^{\,n} satisfy the hypotheses needed so that the remainder after NN terms obeys ∣RN∣≤∣r∣ N+1|R_N|\le |r|^{\,N+1}? (a) −1<r<1,  r≠0-1<r<1,\;r\neq0 (b) −1<r<0-1<r<0 (c) 0<r<10<r<1 (d) 0<r<120<r<\tfrac12

Related theory

Browse the problem library