際際滷

仝親僥々のための慌宥冱�Z
Common Language for the
Science
シグマ (Σ) �催とパイ (Π) �催

mikawaya
換邦慌岻
t2@okayama-u.ac.jp

親僥のための慌宥冱囂

? 方　僥　　徭隼親僥のための慌宥冱囂
仝�T親僥の慌宥冱�Zとしての方僥の�k条と方尖親僥への婢�_々�冩梢旗燕宀�互�鳧�匯隻�
http://www.iias.or.jp/research/project/2011_03.html

とすれば

? �y�僥　　親僥�徭隼、芙氏、繁猟�の
ための
　　　　　　　慌宥冱�Z

シグマ�催

? 峠譲のために弌僥丕 5 定、 6 定の�g圷
�麻はできる
n � H23 �y��紛��Y 2 �、屎盾楕 96% �
‘x
i =1
i = x + x2 + ? + xn

? 詳�~郡鬈�
n
n(n + 1)
‘k = 2
k =1

n
n(n + 1)(2n + 1)
‘k =
k =1
2

6

2
n
? n(n + 1) ?
‘k = ? 2 ?
k =1
3

? ?

なぜ　シグマ� Σ �

n

‘a
k =1
k = a1 + a2 + ? + an


n

‘a
k =1
k = a1 + a2 + ? + an
n

?A k =
k =1
n

?A k =
k =1


n

‘a
k =1
k = a1 + a2 + ? + an
n

?A k = A1 “ A2 “ ? “ An
k =1
n

?A k = A1 ” A2 ” ? ” An
k =1


n

‘a
k =1
k = a1 + a2 + ? + an
n

?A k = A1 “ A2 “ ? “ An
k =1
n

?A k = A1 ” A2 ” ? ” An
k =1
n

’a
k =1
k =


n

‘a
k =1
k = a1 + a2 + ? + an
n

?A k = A1 “ A2 “ ? “ An
k =1
n

?A k = A1 ” A2 ” ? ” An
k =1
n

’a
k =1
k = a1 ? a2 ?? ? an


n

‘a
k =1
k = a1 + a2 + ? + an ‘ Sum
n

’a = a1 ? a2 ?? ? an ’
k =1
n
k
Product
?A k = A1 “ A2 “ ? “ An
n
k =1

’Aa ==Aa”～A ”?”a
n a ～～
k 1 2 n
?1
k=
k =1
k ? A 1 2 n


n

‘a
k =1
k = a1 + a2 + ? + an
n

?A k = A1 “ A2 “ ? “ An
k =1
n

?A k = A1 ” A2 ” ? ” An
k =1
n

’a
k =1
k = a1 ～ a2 ～ ? ～ an

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親僥のための慌宥冱囂

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