__________________________________________________ 数列求和常用公式: 1、1+2+3+......+n=n×(n+1)÷2 2、12+22+32+......+n2=n(n+1)(2n+1)÷6 3、 1+2+3+......+n=( 1+2+3+......+n) =n×(n+1)÷4 4、 1×2+2×3+3×4+......+n(n+1) =n(n+1)(n+2)÷3 5、 1×2×3+2×3×4+...+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 1111 8) + + + =1-1/(n+1)=n÷(n+1) 22×33×4n(n+1)3333222__________________________________________________ __________________________________________________ 11119) + + + 1+21+2+31+2+3+41+2+3+4+…+n2222 = + + + =(n-1) ÷(n+1) 2×33×44×5n(n+1)123(n-1)2×3×4×…(n-1) 10) + + + = 1×22×32×3×42×3×4×…×(n-1)2×3×4×…×n 11)1+3+5+..........(2n-1)=n(4n-1) ÷3 12)1+3+5+..........(2n-1)=n(2n-1) 13)14+24+34+..........+n4=n(n+1)(2n+1)(3n2+3n-1) ÷30 14)15+25+35+..........+n5=n2 (n+1)2 (2n2+2n-1) ÷ 12 15)1+2+2+2+......+2=2 23n(n+1)33332222222 – 1 __________________________________________________ 本文来源:https://www.wddqw.com/doc/06ddeab96b0203d8ce2f0066f5335a8102d2663b.html