Question 983550
{{{A[2]=1/2-1/3}}}
{{{A[3]=1/3-1/4}}}
{{{A[4]=1/4-1/5}}}
.
.
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{{{A[98]=1/98-1/99}}}
{{{A[99]=1/99-1/100}}}
{{{A[100]=1/100-1/101}}}
So then adding all of the terms will eliminate all of the middle terms and leave you with the first and last term.
{{{S=1/2-1/101}}}
{{{S=101/202-2/202}}}
{{{S=99/202}}}