求解一道DS奇偶性数学题

kurisuika · 发表于 2021-5-26 11:11:26

If S= x+ x^2+x^3+...+X^n, is S even? (S is the sum of all terms in geometric sequence)

(1) x is even
(2) n is even

答案是A
（不明白条件二为啥x的个数是偶数个不能由此确定偶数个x相加 S为偶）

长丝弓 · 发表于 2021-5-26 15:00:43

你是对的

ybmg · 发表于 2021-5-26 15:24:56

应该选D吧

又又又又双叒叕 · 发表于 2021-5-26 20:06:55

x是整数么

james333 · 发表于 2021-5-31 21:45:37

For (1),  x is even implies all x^i are even. S is a sum of even numbers. Therefore S is even.

For (2),  there are two cases:
         Case 1: x is even, from result of (1), S is even
         Case 2: x i odd, implies all x^i are odd. Since n is even and S is a sum of n  (even) odd numbers.
                     Therefore S is even.
In summary, the answer is D

james333 · 发表于 2021-5-31 21:47:50

james333 发表于 2021-5-31 21:45
For (1), x is even implies all x^i are even. S is a sum of even numbers. Therefore S is even.

For ...

Sorry, if x is an integer, the Answer is D. Otherwise, the answer is A.

求解一道DS奇偶性数学题

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