The sum of the finite series [tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex] is 20
Given a finite series:
[tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex]
Recall the properties of summation notation:
Σₙ b. f(n) = b Σₙ f(n) where b is a constant.
Σ (a + b) = Σ a + Σ b
[tex]\sum\limits^p_{n=1} {b} =b.p[/tex] where b is a constant
Using the above summation properties, we can write:
[tex]\sum\limits^{8}_{n=1} {(7-n)}=\sum\limits^{8}_{n=1} {7}-\sum\limits^{8}_{n=1} {n}[/tex]
=7 . 8 - (1+2+3+ ...+8)
= 56 - 8/2 (1+8)
= 56 - 4 . 9
= 56 - 36 = 20
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