Answer:
$10
Step-by-step explanation:
Since 6 cost four dollars 3 would cost 2 dollars multiply 3 to get 15 bananas and 2 to get $10
16 1/3 is bigger than 1/4
1) false
2)true
3)-1.346
<span>4)<span><span>x=−5</span><span>x=-5</span></span></span>
<span>5)<span>x=3</span></span>
<span>6)x =~ 3.91 </span>
<span>7) x = 162.69 </span>
<span>hope I helped :)</span>
7)
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
