I'll do problem 13 to get you started.
The expression 
is the same as 
Then we can do a bit of algebra like so to change that n into n-1
This is so we can get the expression in a(r)^(n-1) form
- a = 8/7 is the first term of the geometric sequence
- r = 2/7 is the common ratio
Note that -1 < 2/7 < 1, which satisfies the condition that -1 < r < 1. This means the infinite sum converges to some single finite value (rather than diverge to positive or negative infinity).
We'll plug those a and r values into the infinite geometric sum formula below
S = a/(1-r)
S = (8/7)/(1 - 2/7)
S = (8/7)/(5/7)
S = (8/7)*(7/5)
S = 8/5
S = 1.6
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Answer in fraction form = 8/5
Answer in decimal form = 1.6
Answer: x1=1 x2=-2 and x3=2
Step-by-step explanation:
1st x1=1 is 1 of the roots , so
F(1)=1-1-4+4=0 - true
So lets divide x^3-x^2-4x+4 by (x-x1), i.e (x^3-x^2-4x+4) /(x-1)=(x^2-4)
x^2-4 can be factorized as (x-2)*(x+2)
So x^3-x^2-4x+4=(x-1)*(x^2-4)=(x-1)(x-2)*(x+2)
So there are 3 dofferent roots:
x1=1 x2=-2 and x3=2
K=am+3mx
K=m(a+3x)
m=K/(a+3x)
Answer: m=K/(a+3x)
Answer:6
Step-by-step explanation:
10-:1(2)/(3)
Answer:
k = 2
Step-by-step explanation:
Given that x = - 1 is a root of the equation, then it satisfies the equation.
Substitute x = - 1 into the equation and solve for k, that is
3(- 1)² - 2k - 2(- 1) - 1 = 0
3 - 2k + 2 - 1 = 0
- 2k + 4 = 0 ( subtract 4 from both sides )
- 2k = - 4 ( divide both sides by - 2 )
k = 2
