Question 1023304
S = {{{(1/3)(1-1/4)+(1/3)(1/4-1/7)+(1/3)(1/7-1/10)}}}+...+ {{{(1/3)(1/2011-1/2014) + (1/3)(1/2014-1/2017)}}}

={{{(1/3)}}}*({{{1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10}}}+...+ {{{1/2011-1/2014 + 1/2014-1/2017}}})

={{{(1/3)(1-1/2017)}}} = S

But {{{S= (1/3)(2016/2017) = 672/2017 }}}= 0.333168... >0.3, and also 

{{{S = (1/3)(2016/2017) < 1/3 = 0.33333}}}....< 0.4

Hence,

0.3 < S < 0.4.