The series 6 + 3 + 3/2 + 3/4 +... converges to the sum...?
I have been trying and I can't figure out how to solve this problem. =(
I want to make this clear: I am not looking for the answer, just some help. Thanks!
2007-08-21 02:23:53 · 5 answers · asked by Jenny V. 2 in Science & Mathematics ➔ Mathematics
This is a geometric series with common quocient 1/2. Something like
a + aq + aq^2 + aq^3....., where |q| <1. We know such series converge to a/(1 -q). In your case, a = 6 and q = 1/2. So, your series converges to 6/(1 -1/2) = 6/(1/2) = 12
2007-08-21 03:02:32 · answer #1 · answered by Steiner 7 · 0⤊ 0⤋
S=9+3/2(1+1/2+1/4++++) = 9 + 3/2( 1/(1/2) = 12
2007-08-21 02:34:27 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
= 6 + 3 + 3/2 + 3/4
Determine the least common denominator. In this case it's 4.
= 24/4 + 12/4 + 6/4 + 3/4
Then the sum of the numerators will the new numerator of the new fraction.
= 45/4
Then transform the fraction to its proper form.
= 11 1/4
2007-08-24 22:56:51 · answer #3 · answered by Jun Agruda 7 · 3⤊ 0⤋
2x^2 - 8x + 2y^2 + 12y - 6 = 0 Use a technique suggested as ending up the sq.. upload 6 to the two aspects. 2x^2 - 8x ............+ 2y^2 + 12y........... = 6 factor the two out of each. 2(x^2 - 4x ..........) + 2 ( y^2 + 6y ............) = 6 Pull out the 4, divide it by ability of two, sq. the effect. 4/2 = 2......sq. it...2^2 is 4. upload 4 interior the parenthesis. Do the comparable with the 6 in front of y. 6/2 = 3....3^2 = 9. upload 9 interior the parenthesis with the y^2. you're making suitable sq. trinomials, in different words...the trinomials may well be factored right into a binomial squared. 2(x^2 - 4x + 4) + 2 ( y^2 + 6y + 9) = 6 + 8 + 18 We upload 8 and 18 to the main appropriate area to stability the equation because of the fact on the LEFT area, in case you distribute the two's, you get 2x^2 - 8x + 8 + 2y^2 + 12y + 18. See how the 8 and 18 weren't interior the unique ? 2(x-2)^2 + 2(y+3)^2 = 32 typical equation of a circle is (x-h)^2 + (y-ok)^2 = r^2 so divide each little thing by ability of two. the middle is (h,ok) and the radius is r. (x-2)^2 + (y+3)^2 = sixteen so the middle is (2,-3) and the radius is 4. wish this permits and stable success this 3 hundred and sixty 5 days !
2016-12-12 08:28:40 · answer #4 · answered by Anonymous · 0⤊ 0⤋
6 + 3 + 3/2 + 3/4 +... =
6*(1+1/2+1/4+1/8....)
Got it?
2007-08-21 02:33:37 · answer #5 · answered by ? 5 · 0⤊ 0⤋