Mathematies questions

(a)
(3 + 4×0.1)+(6 + 8×0.1)+(9 + 12×0.1)+...+(96 + 128×0.1)+(99 + 132×0.1)
= (3 + 6 + 9 + ... + 96 + 99) + (4×0.1 + 8×0.1 + 12×0.1 + ... +128×0.1 +132×0.1)
= 3 × (1 + 2 + 3 + ... + 32 + 33) + 4 × 0.1 × (1 + 2 + 3 + ... + 32 + 33)
= (3 + 0.4) × [33 × (33 + 1) / 2]
= 3.4 × 561
= 1907.4


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(b)
10000 - (1x0.5 + 2) - (2x0.5 + 3) - (3x0.5 + 4) - ... -(98x0.5 + 99) - (99x0.5 + 100)
= 10000 - (1x0.5 +2x0.5 + 3x0.5 + ... 99× 0.5) - (2 + 3 + 4 + ..... + 100)
= 10000 - 0.5 × (1 + 2 + 3 + ... + 99) - (1 + 2 + 3 + .... + 99) + 1 - 100
= 9901 - 1.5 × (1 + 2 + 3 + ... + 99)
= 9901 - 1.5 × [99 × (99 + 1) / 2]
= 9901 - 7425
= 2476


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(c)
Let f(x) = x²⁰¹¹

When f(x) = x²⁰¹¹ is divided by (x - 1), the remainder
= f(1)
= 1²⁰¹¹
= 1

Put x = 8 :
When 8²⁰¹¹ is divided by (8 - 1), the remainder = 1
i.e. when 8²⁰¹¹ is divided by 7, the remainder = 1

Hence, 8²⁰¹¹ days are equal to n weeks and 1 days,
where n is an integer.

The day after Sunday is Monday.
Then, the day after 8²⁰¹¹ days is Monday .

2015-04-06 18:08:51 補充：
(c)
8x8x8x8x8x8x8...(2011 times)
= 8^2011

How about question a & b?

c哥題同 qid=7015040500011 嘅第41c 有d似

請問清楚 (c) part 的題目，只是問 8 這麼簡單？

其實問 8 的幾多次方都得～

答案都是 Monday。

因為 8 = 7 + 1，
8ⁿ = (7 + 1)ⁿ = 7(M) + 1

學過二項式定理 (binomial theorem) 就知道。

2015-04-06 16:51:17 補充：
無錯啦～
你更新了題目就更合理！

不過以上己經解答了～

你也可以來意見欄討論一下～