Answer:
1/5.
Explanation:
Note that the sum of infinite geometric series is equally to: a/ (1 - r). Where a = first term and r is the common ratio.
Hence, if f(x) = 3/(1 - 5x) ^2. Therefore, taking the another derivative of f(x)` = 30/ (1 - 5x)^3.
Also, f(x)`` = 450/ ( 1 - 5 )^4 and f(x)``` = 9000( 1 - 5x)^5 and f(x)```` = 225000/( 1 - 5x)^6.
If we are to use the Taylor's series formula then;
F(0) + f'(0) + f"(0)/2! × x^2 + f'''(0)/3! × x^3.
[ NOTE: f(0) = 3, f''(0) = 30, f'''(0) = 9000, f''''(0) = 225000].
450/2! = 225, 9000/ 3! = 1500 and 225000/4! = 9375..
Which gives; 3 + 30x + 225x^2 + 1500x^3 + 9375x^4. The ratio test will then give us our answer as 1/5.
As stated above, alternatively we can make use of the sum of geometric series where |x| < 1/5
Answer:
-5
Step-by-step explanation:

Hope this helps
First, you must distribute 2(3x-1).
To do that, you will multiply 2•3x, and 2•-1 because you are taking the number outside of the parentheses and multiplying (distributing) it to all the numbers inside
After distributing, the left side of your inequality will be 6x-2
Now you have

To find the value of x, you must subtract an x value from both sides of the equation, as well as a constant from each side.
so you have

And that will make the equation

Now, divide the variable side, ***BUT, because you are dividing by a negative number in an inequality, the inequality will switch sides.
Then, the value of x is greater than or equal to 2
Answer:
1. 17,20
2. 40,80
Step-by-step explanation:
1. 5+3=8
8+3=11
11+3=14
14+3=17
17+3=20
pattern is +3
2. 2.5*2=5
5*2=10
10*2=20
20*2=40
40*2=80
pattern is *2