[DSE 2021] 大家準備好瘋狂做 數學 未呢? [5]

1001 回覆
1 Like 9 Dislike
2020-09-24 01:08:33
想問象限問題 拆兩件抵銷 點睇中間既數字+到去邊?

cos1 +cos3+cos5+....+cos359

用cos(180-X) = - cos X 拆兩件抵銷
>cos1...+cos179+cos(180+1)..+cos+(180+179)
呢到就+到179

(sin2)^2+(sin4)^2+...+(sin90)^2

用sin^2+cos^2=1
同sin^2(90-X) = cos^2 X解
拆開中間數字就+到44

應該係小學 單偶數既問題? 應該點搵 係咪最大數字除2 退1格?
冇讀好多年書 好多基本野都唔識 自修緊 可否幫幫手
2020-09-24 16:09:50
用YOUTUBE AD BLOCK +收二手書
白食白拎

下面答案23
44件/2 + Sin^2 90度

係44 中間呢個數字點拎到?
除2 中間數字90/2=45 ? 88/2=44?
但因為雙數跳 45唔存在
所以寫前一個數字 後一個落公式 抵消
2020-09-25 02:21:35

點做
2020-09-25 03:32:08
俾d Permutation, combination + probability 搞到好撚頭痛
2020-09-25 04:57:28
(a)
Note that 7^(4n) ≡ 1 (mod 10) for n is a non-negative integer
1997^2036 ≡ 7^2036 ≡ 7^(4(509)) ≡ 1 (mod 10)
So the last digit of 1997^2036 is 1

Alternatively, consider 1997^2036 = (2000 - 3)^2036.
The first digit of 1997^2036 is the last digit of 3^2036
Note that the last digit of 3^(4n) is 1 for n is a non-negative integer
3^2036 = 3^(4(509))
So the last digit of 1997^2036 is 1
2020-09-25 05:35:00
(b)
log (1997^2036) = 2036 log 1997 = 6719.56974008

1997^2036 = (10^6719)(10^0.56974008)

The first digit of 1997^2036 is the first digit of (10^0.56974008), which is 3
2020-09-25 08:15:50
7既POWER個位數一定係7/9/3/1/7/9/3/1...跟住就秒左
2020-09-25 10:14:32
諗緊有無可能唔用計數機做
2020-09-25 10:45:30
我咁做囉
2020-09-25 10:53:46
原來話b
咁應該冇可能
2020-09-25 10:55:15
講緊first digit..
Number theory高手應該識
但我唔識
2020-09-25 12:23:34
終於唔使zoom
屌好撚憎用zoom教書
2020-09-25 13:18:13

推post
2020-09-25 13:30:42
漏咗3(c) Find the sum of the infinite series
2020-09-25 17:27:19

有冇人識做😭😭😭
2020-09-25 17:59:53
試下右邊用 compound angle formula 拆
2020-09-25 18:04:24

貼返喺度先,廢事又推一輪
2020-09-25 19:23:53
有冇詳細步驟🙏🏼🙏🏼🙏🏼🙏🏼🙏🏼
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