Answer:
The series is convergent answer ⇒ (a)
Step-by-step explanation:
* The series is -8/5 + 32/25 + -128/125 + ........
- It is a geometric series with:
- first term a = -8/5 and common ratio r = 32/25 ÷ -8/5 = -4/5
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = -4/5
∴ IrI = 4/5
∴ IrI < 1
∴ The series is convergent
Answer: A
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Using the Sine rule in all 3 questions
(1)
= 
, substitute values , firstly calculating ∠ B
[ ∠ B = 180° - (78 + 49)° = 180° - 127° = 53° ]
= 
( cross- multiply )
a sin53° = 18 sin78° ( divide both sides by sin53° )
a = 
≈ 22.0 ( to the nearest tenth )
(3)
= , substitute values
= 
( cross- multiply )
45 sinC = 35 sin134° ( divide both sides by 35 )
sinC = 
, then
∠ C = 
( ) ≈ 34.0° ( to the nearest tenth )
(5)
Calculate the measure of ∠ B
∠ B = 180° - (38 + 92)° = 180° - 130° = 50°
= , substitute values
= 
( cross- multiply )
BC sin50° = 10 sin38° ( divide both sides by sin50° )
BC = 
≈ 8.0 ( to the nearest tenth )
