Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. StartFraction 13 Over 2 times 3 EndFraction plus StartFraction 13 Over 3 times 4 EndFraction plus StartFraction 13 Over 4 times 5 EndFraction plus midline ellipsis plus StartFraction 13 Over (n plus 1 )(n plus 2 )EndFraction plus midline ellipsis

Looks like the series is supposed to be

or in condensed form,

Decompose the summand into partial fractions:

So the th partial sum of the series is

As , the second term converges to 0, leaving the value of the infinite series,

unpaid balance is : $149.99-$50 = $99.99 new balance = 149.99+2.62-50 = $102.61 finance charge = 99.99- 0.21/12= $1.75 new balance = 99.99+1.75 = $101.74 average daily balance method average daily balance= 3399.70/30 = $113.32 finance charge = $ 0.21/12ă—113.32 = $1.98 new balance = $149.99-50+1.98 = $101.97