1/( 1x( 1+ 1))+ 1/(2x(2+ 1))+ 1/(3x(3+ 1))+ 1/(4x(4+ 1))+ 1/(5x(5+ 1))............... 1/(n(n+ 1))

Looking for serial numbers

Analysis:

sn =( 1- 1/2)+( 1/2- 1/3)+( 1/3- 1/4)+( 1/4- 1/5).............[ 1/n- 1/(n+ 1)]

= 1- 1/(n+ 1)

Goose sequence

0、2、4、8、 12、 18、24、32、40、50 -

General formula:

an=(n×n- 1)÷2

(n is an odd number)

an=n×n÷2

(n is an even number)

The first n terms and formulas:

tin

=

(n- 1)(n+ 1)(2n+3)÷ 12

(n is an odd number)

tin

=

n(n+2)(2n- 1)÷ 12

(n is an even number)

The grand sequence is derived from Gankun spectrum, which is used to explain the principle of Taiji deduction.

Fibonacci sequence

1、 1、2、3、5、8、 13、2 1、……

general formula

f(n)=( 1/√5)*{[( 1+√5)/2]^n

-

[( 1-√5)/2]^n}

Such a series of completely natural numbers, the general formula is actually expressed by irrational numbers.

You can also find that

S0+S 1+S2+……+Sn-2

= serial number

- 1