Decimal classes can be used. Split clause.

example

1/ 1*2+ 1/2*3+ 1/3* 14......... 1/n(n+ 1)

= 1- 1/2+ 1/2- 1/3+..+ 1/n- 1/n+ 1

=n/n+ 1

As long as it is the summation of fractional series, the split term method can basically be used.

The method of splitting the term is to subtract the reciprocal of the smaller factor from the reciprocal of the larger factor in the denominator, and then compare it with the original general term formula to get the required constant.

2)

superposition method

What is the general formula of 1 36 1 1 5? ...

a2-a 1=2

a3-a2=3

a4-a3=4

a5-a4=5

3)

Ann =

a6-a5=6

..

an-a(n- 1)=n

a2-a 1+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)+..+(an-a(n- 1))

=2+3+4+..+n

an-a 1=(n+2)(n- 1)/2

an=(n^2+n)/2

3)

Formula method

Sn=an^2+bn

an=Sn-S(n- 1)

Example:

a 1=3

Sn=n^2+2n

s(n- 1)=(n- 1)^2+2(n- 1)

an=2n+ 1，

4) patchwork method

an=3a(n- 1)+2

(an+ 1)= 3(a(n- 1)+ 1)

(an+ 1)/(a(n- 1)+ 1)= 3

An+ 1 is a geometric series.

For example:

an =(a(n- 1)/(2a(n- 1)+2)

1/an =(2a(n- 1)+2)/a(n- 1)

=2+2/a(n- 1)

( 1/an+2)= 2( 1/a(n- 1)+2)

((1/an)+2) is a geometric series.

There are many = = recursive methods.