Because b^6 is present in both terms, we can factor it out.
b^6(7 + 12)
Combine like terms.
b^6(19)
Rearrange.
19b^6 is the fully simplified form of the given expression.
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
Easy way is to look at the term with the highest exponent. The exponent determines the number of roots. Some might be double roots. THough not all of then will be real. The imaganry ones come in pairs
Examples:
x^4 - 4 roots
x^7 - 7 roots
x^3 - 3 roots
Answer: 
Step-by-step explanation:
The formula to find the final amount after getting simple interest :
, where P is the principal amount , r is rate of interest ( in decimal )and t is time(years).
Given : Justin deposited $2,000 into an account 5 years ago.
i.e. P = $2,000 and t= 5 years
He has just withdrawn $2,876.
i.e. we assume that A = $2876
Now, Put all the values in the formula , we get
In percent, 
hence, He earned of interest on account.
