Question 1185156
Express as a fraction in simplest form:
{{{8+16+24}}}+…+{{{784}}}/{{{6+12+18}}}+…+{{{588}}}


numerator is:

{{{8+16+24}}}+…+{{{784}}}-> find nth term formula

{{{a[n]=8+8(n-1)}}}
{{{a[n]=8+8n-8}}}
{{{a[n]=8n}}}

last term is {{{784}}}, so {{{n}}} is

{{{784=8n}}}
{{{n=784/8}}}
{{{n=98}}}

denominator is:

{{{6+12+18}}}+…+{{{588}}}

{{{a[n]=6+6(n-1)}}}
{{{a[n]=6+6n-6}}}
{{{a[n]=6n}}}

last term is {{{588}}}, so{{{ n}}} is
{{{588=6n}}}
{{{n=98}}}-> there are {{{98}}} terms in both numerator and denominator


then sum of each sequence is:

{{{sum(8n, n=1,98)= 38808}}}

{{{sum( 6n,n=1,98) = 29106}}}

finally, you have  

{{{38808/29106=4/3}}}