Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
<span>To solve for the given, </span>40, 800 ÷ 10 in unit form and standard form
<span>in unit form and standard form </span>
<span>We can first standardize the given into a equation form which will be: </span>
<span>1. 40,800 / 10 which yield 4,080 </span>
<span>40,800 x 10 = 4080 </span>
<span>Notice the amount of zero the value of 40,800 decreased. </span>
<span>2. The standard form then is 4080 </span>
<span>3. The word form of the quotient is four thousand eighty..<span>
</span></span>
Cross sections of spheres are cicles. Therefore, if cut parallel to the ends, CYLINDER also has cross sections that match that of a circle.
Answer:
Base = 353.55 sq cm
Step-by-step explanation:
10 by 10 triangle = 45 45 90 traingle
hypotenuse = 10√2
A = 10√2 by 25
