`1/15 + 1/105 + 1/315 + .... + 1/9177`
`=1/(1.3.5) + 1/(3.5.7) + 1/(5.7.9) +...+ 1/(19.21.23)`
`=1/4.(1/(1.3.5) + 1/(3.5.7) + 1/(5.7.9) +...+ 1/(19.21.23))`
`=1/4.(1/1.3 - 1/3.5 + 1/3.5 - 1/5.7 + 1/5.7 - 1/7.9 +...+ 1/19.21 - 1/21.23)`
`=1/4.(1/3-1/21.23)`
`=1/12-1/1932<1/12`