題:
maths***
2006-10-14 15:37:07 UTC
1. (-1)^﹝(2N+3)-(N+1)﹞..........................................答案係 -1(N係奇數)
1(N係偶數)
2. (-1)^ -2N + (-1)^N................................................答案係 0(N係奇數)
2(N係偶數)
3.N係整數,求證9(N+1) - (N+5)係偶數
一 回答:
myisland8132
2006-10-14 15:42:39 UTC
1.

(-1)^﹝(2N+3)-(N+1)﹞

=(-1)^(N+2)

if N is odd

N+2 is odd

so

(-1)^(N+2)

=-1

if N is even

N+2 is even

so

(-1)^(N+2)

=1

2.

(-1)^ (-2N) + (-1)^N

if N is odd

-2N is even

(-1)^ (-2N) + (-1)^N

=1-1

=0

if N is even

-2N is even

(-1)^ (-2N) + (-1)^N

=1+1

=2

3.N係整數,求證9(N+1) - (N+5)係偶數

9(N+1) - (N+5)

=9N+9-N-5

=10N+4

=2(5n+2)

is a even number


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