<PRE><B>Question 842594</B>
The savings for any particular week is
$4 times the number of that week
Let {{{ n }}} = the week number.
{{{ 4n }}} is the savings for week {{{ n }}}
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You are letting {{{ n }}} go from {{{ 1 }}} to {{{ 52 }}}
So, the expression for total savings looks like:
4*( 1 + 2 + 3 + 4 + 5 + . . .  )
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The formula for the sum of all integers from
1 to n is {{{ ( n*( n+1 ))/2 }}}
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Let {{{ S }}} = total savings for {{{ n }}} weeks
{{{ S = ( 4n*( n+1 ) )/2 }}}
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Now let {{{ n = 52 }}}
{{{ S = ( 4*52*53 )/2 }}}
{{{ S = 11024/2 }}}
{{{ S = 5512 }}}
The savings for 52 weeks is $5,512

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