`3/(1times2)+7/(2xx3)+13/(3xx4)+21/(4xx5)+31/(5xx6)+43/(6xx7)`
`=(1/(1times2)+1)+(1/(2xx3)+1)+(1/(3xx4)+1)+(1/(4xx5)+1)+(1/(5xx6)+1)+(1/(6xx7)+1)`
`=(1/(1times2)+1/(2xx3)+1/(3xx4)+1/(4xx5)+1/(5xx6)+1/(6xx7))+(1+1+1+1+1+1)`
`=(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)+6`
`=1-1/7+6`
`=48/7`