Sigma notation - Mathcentre

Answers
1.
(a)
(b)
(c)
(d)
(e)
(f)
2. 30.
5∑
n 3 = 1 3 + 2 3 + 3 3 + 4 3 + 5 3
n=1
5∑
3 n = 3 1 + 3 2 + 3 3 + 3 4 + 3 5
n=1
4∑
(−1) r r 2 = −1 2 + 2 2 − 3 2 + 4 2
r=1
4∑ (−1) k+1
2k + 1 = 1 − 1 + 1 − 1 3 5 7 9
N∑
x 2 i = x2 1 + x2 2 + x2 3 + . . . + x2 N
k=1
i=1
N∑
f i x i = f 1 x 1 + f 2 x 2 + f 3 x 3 + . . . + f N x N
i=1
3.
5∑
1
(a) + 1 + 1 + 1 + 1 = 1
1 2 3 4 5
k
k=1
(b) −1 + 2 − 3 + 4 − 5 + 6 − . . . + 20 =
20∑
k=1
(−1) k k
(c) (x 1 − µ) 2 + (x 2 − µ) 2 + (x 3 − µ) 2 + (x 4 − µ) 2 =
4∑
(x k − µ) 2
k=1
5.
4∑
k=1
1
(2k + 1)(2k + 3) = 1
(3)(5) + 1
(5)(7) + 1
(7)(9) + 1
(9)(11)
c○ mathcentre July 18, 2005 10