1) the sum (S) of the first "n" positive integers partly varies directly as "n" and
partly varies directly as the square of "n"
(a) by considering the sums when n=2 and n =3, find an equation connecting n and S
(b) Find the sum of all the integers from 1 to 50
F.4.Maths Variartions (40)
2010-09-20 12:46 am
回答 (1)
2010-09-20 1:17 am
✔ 最佳答案
1a)S=an+bn^2 , where a and b are constants
when n=2, the sum of 1,2 are 3
when n=3, the sum of 1,2,3 are 6
Sub n=2,S=3 and n=3,S=6:
3=2a+4b...(1)
6=3a+9b...(2)
(1)*3-(2)*2:
12b-18b=9-12
-6b=-3
b=1/2 and a=1/2
S=(n+n^2)/2
b)
S=(50+50^2)/2=1275
收錄日期: 2021-04-16 12:07:54
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https://hk.answers.yahoo.com/question/index?qid=20100919000051KK01250