Find the first three terms and the eigth term of these...?

Question

FYI..I have already completed several..Am unsure about a couple of them..I simly want to check myself and learn something. This is for an online College Algebra Class...This necessarily needs to be completed and unerstood today as I have an exam coming up on Tuesday; my Professor is inaccessible today. Thanks for your help.

1.) n!/(n-1)!

2.)a(subscrpit)1=2, a(subscript)n = 3a(subscript)n-1

3.) a(subscript)1=2, a(sub)n = (-3)na(sub)n-1

4.) a(sub)1=1, a(sub)2=4,a(sub)n=(a(sub)n-1)(a(sub)n-2). Find a3,a4,a5 only.

5.) 100!/98!2!

6.) written above: 6 ∑ Written below: k=1. Written to the right of: 1/k(k+1)

7.) written above: 8 ∑ written below: n=2. Written to the right of: In n/n+1

8.) Write this is summation notation: 1 - 2/3 + 4/9 - 8/27 + 16/81 - 32/243

Answer 1

1.) n!/(n-1)!
1!/(1-1)!=1/1=1
2!/1!=2
3!/2!=3

8!/7!=8


2.)a(subscrpit)1=2, a(subscript)n = 3a(subscript)n-1
a_1=2
a_n=3a _n-1
a_2=3a_1 =3*2=6

a3=3*a_2=3*6=18

a_8=3*a_7=?


3.) a(subscript)1=2, a(sub)n = (-3)na(sub)n-1
a_1=2
a_n=-3n a_n-1
a_2=-3*2* 2=-12

a_3=-3*3*(-12)= 108

a_8=-3*8*a_7=?


4.) a(sub)1=1, a(sub)2=4,a(sub)n=(a(sub)n-1)(... Find a3,a4,a5 only.
a_3=a_2=4
a_4=4
a_5=4


5.) 100!/98!2!
=99*100/2=99*50= 4950


6.) written above: 6 ∑ Written below: k=1. Written to the right of: 1/k(k+1)

1/1*2+1/2*3+1/3*4+1/4*5+....

try to write as two fractions

1/k(k+1)=-1/(k+1)+1/k

Then calcel like terms from expansion
7.) written above: 8 ∑ written below: n=2. Written to the right of:
In n/n+1
ln2/3+ln3/4+ln4/5+..+ln8/9


8.) Write this is summation notation: 1 - 2/3 + 4/9 - 8/27 + 16/81 - 32/243
sigma from k= 0 up to k=5 of (-2/3)^k