数列求和常用公式:
1)1+2+3+......+an=n(an+1)÷2
2)12+22+32+......+n22=n(n+1)(2n+1)÷6
3) 13+23+33+......+n3=( 1+2+3+......+n)3 =n2*(n+1)2÷4
4) 1*2+2*3+3*4+......+n(n+1)
=n(n+1)(n+2)÷3
5) 1*2*3+2*3*4+3*4*5+......+n(n+1)(n+2)
=n(n+1)(n+2)(n+3)÷4
6) 1+3+6+10+15+......
=1+(1+2)+(1+2+3)+(1+2+3+4)+......+(1+2+3+...+n)
=[1*2+2*3+3*4+......+n(n+1)]/2=n(n+1)(n+2) ÷6
7)1+2+4+7+11+......
=1+(1+1)+(1+1+2)+(1+1+2+3)+......+(1+1+2+3+...+n)
=(n+1)*1+[1*2+2*3+3*4+......+n(n+1)]/2
=(n+1)+n(n+1)(n+2) ÷6
8)1/2+1/2*3+1/3*4+......+1/n(n+1)
=1-1/(n+1)=n÷(n+1)
9)1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+......+1/(1+2+3+...+n)
=2/2*3+2/3*4+2/4*5+......+2/n(n+1)
=(n-1) ÷(n+1)
10)1/1*2+2/2*3+3/2*3*4+......+(n-1)/2*3*4*...*n
=(2*3*4*...*n- 1)/2*3*4*...*n
11)12+32+52+..........(2n-1)2=n(4n2-1) ÷3
12)13+33+53+..........(2n-1)3=n2(2n2-1)
13)14+24+34+..........+n4
=n(n+1)(2n+1)(3n^2+3n-1) ÷30
14)15+25+35+..........+n5
=n2 (n+1)2 (2n2+2n-1) ÷ 12
15)20+21+22+23+......+2n=2(n+1) – 1