math
posted by s on .
determine the difference between the sum of the infinite geometric series 186+22/3...and the sum of the first 6 terms of the series (round to 3 decimal places)
first i did
S=18/ (1+1/3)= 13 1/2
Sn= 18(1+(1/3)^6)
_____________
1 + 1/3
= 13 14/27
13 1/2  13 14/27 = 1/54
what did i do wrong?

your formula for Sn is wrong
it is
Sn = a(1  r^n)/(1r)
= 18(1  (1/3)^6)/(1+1/3)
= 18 (1  1/729)/(4/3)
= 18(728/729)(3/4)
= 364/27
((you had 365/27))
so the difference is │364/27  27/2│
= 1/54
It didn't say which way the subtraction was supposed to go, so I took the absolute value. 
ohh, i thought 1( 1/3)= 1+(1/3)
thanks so much 
not 1( 1/3) but 1( 1/3)^6
you have to do the power first, so (1/3)^6 = +1/729, now you subtract it...