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 connnecting n
and S.
b) Find the sum of all the integers from 1 to 50.
maths
2010-05-15 4:47 am
回答 (1)
2010-05-15 5:03 am
✔ 最佳答案
a) Let (Sn) = (k1)n + (k2)n^2
when n = 2 ,
(S2) = 2(k1) + 4(k2) = 1+2 = 3......(1)
when n = 3 ,
(S3) = 3(k1) + 9(k2) = 1+2+3 = 6......(2)
(2)*2 - (1)*3 :
(18 - 12)(k2) = 6*2 - 3*3
(k2) = 1/2
By (1) : 2(k1) + 4(1/2) = 3
(k1) = 1/2
So (Sn) = (k1)n + (k2)n^2
(Sn) = (1/2)n + (1/2)n^2
(Sn) = (n + n^2) / 2
(Sn) = n(n+1)/2
b)
(S 50) = (50)(50+1)/2 = 1275
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