This is not true. The infinite series

converges if and only if the sequence of its partial sums converges. The

-th partial sum is

but clearly this diverges as

gets arbitrarily large.
Answer:
m∠6 = 116°
Step-by-step explanation:
<u>first find x:</u>
7x - 17 = 2x + 78
subtract 2x from both sides: 5x - 17 = 78
add 17 to both sides: 5x = 95
divide by 5: x = 19
<u>plug x into 7x - 17</u>
7(19) - 17 = 116
∠6 and 7x - 17 are vertical angles and therefore congruent, so m∠6 also = 116°
4t+2c=200
2t+7c=400
I will solve for c in terms of t first
4t+2c=200
2c=200-4t
c=100-2t
Then I will substitute this in for c in the second equation to make it single variable
2t+7c=400
2t+7(100-2t)=400
2t+700-14t=400
300t=12
t=25
Tables cost $25 each
Plug t back into one of the ORIGINAL equations to find the cost of chairs
4(25)+2c=200
100+2c=200
2c=100
c=50
Chairs cost $50 each
Hope this helps! :)
SOLUTION
Given the question in the question tab, the following are the solution steps to get the rental cost for each movie and each video game.
Step 1: Write the representation for the two rentals
Let m represents movies
Let v represent video games
Step 2: Write the statements in form of a mathematical equation

Step 3: Solve the equations above simultaneously using elimination method to get the values of m and v

Rental cost for each movies is $3.25
Rental cost for each video games $5.50
Volume
of a rectangular box = length x width x height<span>
From the problem statement,
length = 60 - 2x
width = 10 - 2x
height = x</span>
<span>
where x is the height of the box or the side of the equal squares from each
corner and turning up the sides
V = (60-2x) (10-2x) (x)
V = (60 - 2x) (10x - 2x^2)
V = 600x - 120x^2 -20x^2 + 4x^3
V = 4x^3 - 100x^2 + 600x
To maximize the volume, we differentiate the expression of the volume and
equate it to zero.
V = </span>4x^3 - 100x^2 + 600x<span>
dV/dx = 12x^2 - 200x + 600
12x^2 - 200x + 600 = 0</span>
<span>x^2 - 50/3x + 50 = 0
Solving for x,
x1 = 12.74 ; Volume = -315.56 (cannot be negative)
x2 = 3.92 ;
Volume = 1056.31So, the answer would be that the maximum volume would be 1056.31 cm^3.</span><span>
</span>