简便运算快2/（5*7）+4/（7*11）+6/（16*22）+3/（2*5）+5/（11*16）+7/（22*29)+1/29

Question

简便运算 快
2/（5*7）+4/（7*11）+6/（16*22）+3/（2*5）+5/（11*16）+7/（22*29)+1/29

Answer 1

2/(5*7)+4/(7*11)+6/(16*22)+3/(2*5)+5/(11*16)+7/(22*29)+1/29
=3/(2*5)+2/(5*7)+4/(7*11)+5/(11*16)+6/(16*22)+7/(22*29)+1/29
=(1/2-1/5)+(1/5-1/7)+(1/7-1/11)+(1/11-1/16)+(1/16-1/22)+(1/22-1/29)+1/29
=1/2-1/5+1/5-1/7+1/7-1/11+1/11-1/16+1/16-1/22+1/22-1/29+1/29
=1/2
附公式1/n(n+a)=1/a[1/n-1/(n+a)]
由此公式可得a/n(n+a)=a*1/a[1/n-1/(n+a)]=1/n-1/(n+a)