You can try to show this by induction:
• According to the given closed form, we have 
, which agrees with the initial value <em>S</em>₁ = 1.
• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume
and
We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or
From the given recurrence, we know
so that
which is what we needed. QED
Answer:
DANG some of these questions are from like 2017 and still havent been answerd
Step-by-step explanation:
Answer:
Step-by-step explanation:
To isolate r, we're going to need to do some algebraic manipulation.
Multiply both sides by r:
Divide both sides by a:
Hope this helps!
Answer:
200 people attended screen 1
150 to screen 2 and 150 to screen 3
for question 2:it's 265.1
Since this problem talks about rates of change, then the concept of calculus is very useful. But first, let's find at least two equations in order to solve this system. The first one is the area of a triangle written as
A = 1/2 ab sin θ, where a and b are the sides that from the angle θ. So, we substitute a=6 and b=10. That makes it:
A = 1/2 (6)(10)sin θ = 30 sin θ
Now, you differentiate implicitly (both sides simultaneously) with respect to time.
dA/dt = 30 cosθ (dθ/dt)
We replace dθ/dt = 0.06 rad/s, as mentioned in the problem. Then, the rate of change of the area of the triangle when θ = π/3 rad with respect to time is
dA/dt = 30cos(π/3) (0.06)
dA/dt = 1.8 m²/s
Therefore, the rate of change of the area of the triangle is 1.8 m² per second.
