10-5又1⼀2-1又1⼀4-2⼀3-1⼀8等于多少

a3-a1 = 10-1 = 9 = 32 a4-a2 = 20-4 = 16 = 42 a5-a3 = 35-10 = 25 = 52 . an-1 -an-3 = (n-1)2 an - an-2 = n2 上式相加：an +an-1 -a2 - a1=32+42+52+...+n2 an +an-1 =1+4+32+42+52+...+n2 =12+22+32+42+52+...+n2 = n(n+1)(2n+1)/6.① a1=1 a2=1+(1+2) a3=1+(1+2)+(1+2+3) . an-1 = 1+(1+2)+(1+2+3)+...+(1+2+3+...+n-1) an = 1+(1+2)+(1+2+3)+...+(1+2+3+...+n-1) + (1+2+3+...+n) 得：an - an-1 = 1+2+3+...+n =n(n+1)/2 .② ①+②得：2an = n(n+1)(2n+1)/6 + n(n+1)/2 an = n(n+1)(n+2)/6 12+22+32+42+52+...+n2 = n(n+1)(2n+1)/6 ————————————————————————————————————希望帮到你，加油！