Binomial expansion

用戶8880

2007-03-04 8:23 am

1.An eccentric Lottery winner decided to give money to some of the pupils at his former school.Each of the 1100pupils was assigned a different number from 1to1100.
a)At the morning assembly he gave money to each pupil whose number was divisible by 3. Pupil number 3 received $3, pupil number 6 received $6, and so on, each of these pupils receiving a number of $ equal to his or her assigned number. Calculate the total amount of money given out at the morning assembly.

回答 (1)

用戶40379

2007-03-04 10:05 am

✔ 最佳答案

1a) Calculate the total amount of money given out at the morning assembly.
3+6+9+12+……..+1098 [小於或等於1100的中，3的倍數最大為1098，而共有366 個數字]
= (3 + 1098)x366 / 2
= 201483 元

1b) Find the greatest amount of money given to one of the pupils at the afternoon assembly.
50、100、……、1100 [中共有 1000/50 = 22個學生]
第一個學生(50號)獲得 1 元 = 20元
第二個學生(100號)獲得 2 元 = 21元
第三個學生(150號)獲得 4 元 = 22元
…………………..
第22個學生(1100號)獲得 x 元 = 222-1元
222-1 = 221
= 2097152元

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