Презентация, доклад по математике Последовательность, 10 класс

etc.

11

The factorial sequence
fr+1=fr×(r+1), where r=0,1,2,3…… and f0=1

f1=f0×1=1, f2=f1×2=2, f3=f2×3=6

fr=1×2×3×…×r

Factorial r is defined by 0!=1 and (r+1)!=r!×(r+1)

where r=0,1,2,3….. For r≥1, r! is the product of
all the natural numbers from 1 to r.

Read as factorial r or r factorial

n=0:1,0,0,0,0…
n=1:1,1,0,0,0…
n=2:1,2,1,0,0…
n=3:1,3,3,1,0…

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

Pascal`s triangle which will be studied in chapter 9

To find the value that the sequence converges to we use the fact that eventually ( at infinity! ) the ( n + 1 ) th term equals the n th term.

2. What value does the sequence given by

The general term can easily be checked by substituting n = 1, n = 2, etc.

2.

Sigma Notation for a Series

A series can be described using the general term

(a)

(b)

n = 1

n = 2

n = 20