I am stuck at these Math questions.Help!!

[LeQuavina]

1-Find the sum of the following geometric series.Give numerical answers as rational numbers.
a)1 + 1/2 + 1/4 +.....+1/2^n
b)16+4+1+...+1/2^2n
c)81-27+9-....+1/(-3)^n

2-Find the coordinates of the points of intersection of the given straight line with the curve.
a)y=2x-12 , x^2+4xy-3y^2=-27
b)2x-5y=6 , 2xy-4x^2-3y=1

Thank you in advance.

 

[leosco1995]

Q1)

Use the sum to infinity formula.

S = a/1-r where a = first term and r = common ratio

Like in the first case, a = 1 and r = (1/2)/1 = 1/2.

S = 1/ [1-(1/2)]
= 2

Q2) Just solve them simulatenously, like:

a)
y = 2x-12
x^2 + 4xy - 3y^2 = -27

In Place y from (1) into (2)

x^2 + 4x(2x-12) - 3(2x-12)^2 = -27
x^2 + 8x^2 - 48x - 3(4x^2 - 24x + 144) = -27
9x^2 - 48x - 12x^2 + 72x - 432 = -27

..etc. Find x and place it in (1) to get y.

 

[LeQuavina]

Q1)

Use the sum to infinity formula.

S = a/1-r where a = first term and r = common ratio

Like in the first case, a = 1 and r = (1/2)/1 = 1/2.

S = 1/ [1-(1/2)]
= 2

Q2) Just solve them simulatenously, like:

a)
y = 2x-12
x^2 + 4xy - 3y^2 = -27

In Place y from (1) into (2)

x^2 + 4x(2x-12) - 3(2x-12)^2 = -27
x^2 + 8x^2 - 48x - 3(4x^2 - 24x + 144) = -27
9x^2 - 48x - 12x^2 + 72x - 432 = -27

..etc. Find x and place it in (1) to get y.

I don't think we were supposed to use the sum to infinity formula because the answer given at the back of the book is x(1-(-x)^n)/ 1+x

and for Q2) I solved it in that way but I got stuck at 3x^2-24x+405=o