2006-08-13 08:32:20 · 13 answers · asked by David G 1 in Science & Mathematics ➔ Mathematics
15/ 16th, or .9375
2006-08-13 08:41:07 · answer #1 · answered by wellaem 6 · 0⤊ 0⤋
1
2006-08-13 15:40:38 · answer #2 · answered by Steel 2 · 0⤊ 0⤋
Well this is a geometric series. There are many ways to do this.
1. Use a formula;
This is geometric with a = 1/2, r = 1/2
So S_4 = a * ( r^4-1) / (r-1) = 1/2 ( - 15/16) / (-1/2) = 15/16
2. Sum them up the old fashioned way
1/2 + 1/4 + 1/8 + 1/16
=8/16 + 4/16 + 2/16 + 1/16
=(8+4+2+1)/16 = 15/16
3. Notice a pattern.
S_1 = 1/2 = (2-1)/2=(2^1-1)/2^1
S_2 = 1/2+1/4 = (4-1)/4=(2^2-1)/2^2
S_3 = 1/2+1/4+1/8 = (8-1)/8=(2^3-1)/2^3
...
S_n = (2^n-1)/2^n (omiting proof of course)
So S_4 = (2^4-1)/2^4 = 15/16
2006-08-13 16:28:34 · answer #3 · answered by Anonymous · 0⤊ 0⤋
15/16=
8/16+4/16+2/16+1/16
2006-08-13 15:37:27 · answer #4 · answered by Anonymous · 0⤊ 0⤋
15/16
2006-08-13 16:32:03 · answer #5 · answered by Chikky D 4 · 0⤊ 0⤋
15/16
2006-08-13 15:52:17 · answer #6 · answered by Anonymous · 0⤊ 0⤋
15/16
2006-08-13 15:48:19 · answer #7 · answered by samy2k69 1 · 0⤊ 0⤋
15/16
2006-08-13 15:39:30 · answer #8 · answered by jackofalltds 3 · 0⤊ 0⤋
15/16
2006-08-13 15:36:56 · answer #9 · answered by banana music mango 3 · 0⤊ 0⤋
the answer is 15/16
2006-08-13 15:40:02 · answer #10 · answered by echo 2 · 0⤊ 0⤋
The sum, as expressed, is of course 15/16. If you add more terms, the sum gets arbitrarily close to 1.
2006-08-13 16:21:32 · answer #11 · answered by Anonymous · 0⤊ 0⤋