Homework SourseFind the first five partial sums of the given series and det
Find the first five partial sums of the given series and determine whether the series appears tobe convergent or divergent. If it is convergent, find the approximate sum.
1/2-1/4+1/8-1/16+1/32-...
I got
S1=.5
S2=.25
S3-.375
S4=.3125
S5=.3437
So it looks like it\'s converging to a .3 something but I don\'t know how to calculate it from the given information. Could someone help please.
1/2-1/4+1/8-1/16+1/32-...
I got
S1=.5
S2=.25
S3-.375
S4=.3125
S5=.3437
So it looks like it\'s converging to a .3 something but I don\'t know how to calculate it from the given information. Could someone help please.
Solution
vThis is an infinite geometric series where the first term is ¼, and the common ratio \"r\" is ½. The sum is found by the formula: . . . . .a S = -------- . . . .1 - r . . . . .¼ S = -------- . . . .1 - ½ . . . ¼ S = ---- = ½ <==ANSWER . . . ½
