Mathematics

Mathematics

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

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