We have a geometric sequence----------- > <span>{-4, 12, -36, ...}
</span><span>
the formula is a(r)^(n-1)
a------------- >a is the first term------------ > -4
r--------------- > </span><span>is the common ratio------- > 12/(-4)=(-36/12)=-3
n--------------- > is the number of terms
</span>The fifth term is -4[(-3)^(5-1)]=-4[(81]=-324
the answer is -324
You have to use the Pythagorean theorem a squared plus b squared is c squared so 13 squared plus 18 squared equals c squared. 13x13=169 18x18=324 169+324=493 so c squared is 493 to get c you square root 493 which equals 22.2 so the diagonal, c, is 22.2 centimeters long
Answer:
Required solution gives series (a) divergent, (b) convergent, (c) divergent.
Step-by-step explanation:
(a) Given,
To applying limit comparison test, let 
and 
. Then,
Because of the existance of limit and the series 
is divergent since 
where 
, given series is divergent.
(b) Given,
Again to apply limit comparison test let 
and 
we get,
Since 
is convergent, by comparison test, given series is convergent.
(c) Given,
. Now applying Cauchy Root test on last two series, we will get,
- \lim_{n\to \infty}|(\frac{5}{6})^n|^{\frac{1}{n}}=\frac{5}{6}=L_1
- \lim_{n\to \infty}|(\frac{1}{3})^n|^{\frac{1}{n}}=\frac{1}{3}=L_2
Therefore,
Hence by Cauchy root test given series is divergent.
