1×2+2×3+3×4+.......+49×50等于几

Answer 1

1×2+2×3+3×4+.......+49×50  最终结果是 41056

我是写了个程序快速算出来的。

main()

{

int sum=0;

for(int i=1;i<50; i++) {

printf("%d: %d×%d=%d\n",i,i,i+1,i*(i+1));

sum = sum + i*(i+1);

}

printf("Result=%d",sum);

}

Answer 2

过程详细如下。1×2+2×3+3×4+.......+49×50=22+32+42......492+502-1-2-3....-49-50=1+22+32+42......492+502-(1+2+3....+49+50)-1=42925-1275-1=41650-1=41649

Answer 3

an
=n(n+1)
=(1/3)[n(n+1)(n+2)-(n-1)n(n+1)]
Sn
=a1+a2+...+an
=(1/3)n(n+1)(n+2)
1x2+2x3+3x4+...+49x50
=S49
=(1/3)(49)(50)(51)
=41650

Answer 4

解答:an=n²+n
1*2+2*3+3*4+……+49*50
=1²+1+2²+2+3²+3+……+49²+49
=1+2+3+……+49+1²+2²+3²+……+49²
=49*50/2+49*50*99/6=41650