Please help with my Pre-Calculus Homework?

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Lorraine

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3) is referring to an infinite geometric series where IrI < 1

Let Sn = 40 + 40r + 40r^2 + 40r^3........+40r^n = 40(1 + r + r^2 +........+ r^n)
Then Sn/40 = (1 + r + r^2 + ..... + r^n)
And, r Sn/40 = (r + r^2 + r^3 +....+ r^(n+1))

Sn/40 - r Sn/40 = (1 - r^(n +1))
(1 - r)Sn = 40(1 - r^(n + 1))
Sn = 40(1 - r^(n + 1))/(1 - r)

Try it for the limit as n approaches infinity

Sn = 40/(1 - r) Limit (1 - r^(n+1))
Sn = 40/(1 - r) Limit (1) - Limit (0)
Sn = 40/(1 - r)
Sn = 40/(1 - 70/100) = 40/(1 - 7/10) = 40/(3/10) = 40*10/3 = 400/3 ft

Neat huh?
 
3) is referring to an infinite geometric series where IrI < 1

Let Sn = 40 + 40r + 40r^2 + 40r^3........+40r^n = 40(1 + r + r^2 +........+ r^n)
Then Sn/40 = (1 + r + r^2 + ..... + r^n)
And, r Sn/40 = (r + r^2 + r^3 +....+ r^(n+1))

Sn/40 - r Sn/40 = (1 - r^(n +1))
(1 - r)Sn = 40(1 - r^(n + 1))
Sn = 40(1 - r^(n + 1))/(1 - r)

Try it for the limit as n approaches infinity

Sn = 40/(1 - r) Limit (1 - r^(n+1))
Sn = 40/(1 - r) Limit (1) - Limit (0)
Sn = 40/(1 - r)
Sn = 40/(1 - 70/100) = 40/(1 - 7/10) = 40/(3/10) = 40*10/3 = 400/3 ft

Neat huh?
 
Can someone help me solve these problems. It would be best if work was shown.

1)Find the partial sum S9 of: 2.2, 7.4, 12.6,...............43.8

2) Use the binomial theorem to expand and simplify (3a-2b^-1)^5

3) A ball is dropped from a height of 40ft. Each time it strikes the ground, it rebounds to a height 70% of the distance it fell. Find the total distance the ball travels.
 
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