. The series is divergent. To see this, first observe that the series ∑ 1/kn for n = 1 to ∞ is divergent for any integer k ≥ 2.
Now, if we pick a large integer for k, say k > 100, then for nearly all integers n it will be true that 1 > cos(n) > 1/k. Therefore, since ∑ 1/kn is divergent, ∑ cos(n)/n must also be divergent The *summation* is divergent, but the individual terms converge to the number 0.<span>by comparison test since cosn/n <= 1/n is convergent
and 1/n is divergent by harmonic series
so the series is conditionally converget </span>
<u>Step-by-step explanation:</u>
(a) A natural number that is greater than 25 and less than 40
Natural Number : These are numbers starting from 1 or also sometimes from zero and are all positive ! A natural greater than 25 & less than 40 is 30 .
(b) An integer which is less than -5 and a multiple of 2
Integer : An integer is a whole number not a fraction including 0 . It can be positive or negative ! Integer less than -5 and a multiple of 2 is -6.
(c) A rational number between 1 and 2
Rational Number : A number which can be expressed in form of p/q where q is not equal to 0 . A rational number between 1 & 2 is 3/2 .
(d) An irrational number between 8 and 9.
Irrational Number: A real number which is not rational or can't be written in form of p/q . An irrational number between 8 & 9 is
.
B 16 miles an hour
Hope this helps
X + 3y = 7
y = 2
Substitute
x + 3(2) = 7
x + 6 = 7
x = 1
Hope this helps!<span />
Answer:
Hello,
Step-by-step explanation:
Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.
