In view of Exercise 19(a) in Section 2.1, we can write S = 1 + 1/2 + 1/4 + 1/8 +

Question

In view of Exercise 19(a) in Section 2.1, we can write S = 1 + 1/2 + 1/4 + 1/8 + 1/16 + S = 1 + 1/2 (1 + 1/2 = 1/4 + 1/8 + 1/16 +) S = 1 + 1/2 S 1/2 S = 1 5 = 2. This evaluation of the limit avoids the use of Exercise 18 from Section 2.1. Mimicking the preceding line of equalities, consider a different situation. Say that we write R = 1 + 2 + 4 + 8 + 16 + A = 1 + 2(1 + 2 + 4 + 8+ 16 +) R = 1 +2R? R - 2R= 1 R = -1. Is there anything suspicious in this argument? Is there any relationship with the one above? Explain.

Explanation / Answer

the above argument is fully wrong because in

case 1. when S=2 we got , which is somehow, according to expression at infinite , must be nearly equal to 2.

but in case 2. R= -1 , could never be true for the given series of number.

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