1+2=(1+2)×2/2=3的规律?1+2= (1+2)×2/2=31+2+3=（1+3）×3/2=61+2+3+4=（1+4）×4/2=101+2+3+4+5=（1+5）×5/2=15·······································1+2+3+4+5+················n=（1+n）×
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/25 13:06:55
1+2=(1+2)×2/2=3的规律?1+2= (1+2)×2/2=31+2+3=（1+3）×3/2=61+2+3+4=（1+4）×4/2=101+2+3+4+5=（1+5）×5/2=15·······································1+2+3+4+5+················n=（1+n）×
1+2=(1+2)×2/2=3的规律?
1+2= (1+2)×2/2=3
1+2+3=（1+3）×3/2=6
1+2+3+4=（1+4）×4/2=10
1+2+3+4+5=（1+5）×5/2=15
·······································
1+2+3+4+5+················n=（1+n）×n/2
（1）n个连续自然数之和的计算规律用语言叙述是：_________________________.
（2）计算1+2+3+4+··········+99+100
（3）求1+ 1/1+2 + 1/1+2+3 + 1/1+2+3+4 + 1/1+2+3+4+5 +···············+1/1+2+3+4+··········+100的值
1+2=(1+2)×2/2=3的规律?1+2= (1+2)×2/2=31+2+3=（1+3）×3/2=61+2+3+4=（1+4）×4/2=101+2+3+4+5=（1+5）×5/2=15·······································1+2+3+4+5+················n=（1+n）×
（1）首项加末项乘以项数除以2
（2）原式=(1+100)*100/2=101*50=5050
（3）设an=1/(1+2+...+n)=2/(n*(n+1))=(1/2)(1/n-1/(n+1))
所以原式=（1/2）(1-1/2+1/2-1/3+...+1/100-1/101)
=1/2*(1-1/101)=50/101