Find the first four partial sums and the nth partial sum of

Find the first four partial sums and the nth partial sum of the sequence a_n. [Hint: Use a property of logarithms to write the nth term as a difference.]a_n = 8 log

show the work

S1=

S2=

S3 =

S4=

Sn=

Solution

a_n=8log(n/n+1)

using log property which is

log(a/b)= log a- log b

8 log(n/n+1)= 8logn - 8 log(n+1)= log n^8 = log(n+1)^8

patial sums

first we have to fint the terms,and for that we have to plug n=1,2,3,4

8log(1/2),8log(2/3),8log(3/4),8log(4/5)

s₁= 8log(1/2)

s₂=8 log(1/2) + 8 log(2/3)=8(log(1/2)+ log(2/3))= 8log(1/2*2/3)=8log(1/3)

s₃=8log(1/2)+8log(2/3)+8log(3/4)=8log(1/4)

s₄=8log(1/2) + 8log(2/3)+8log(3/4) +8log(4/5)=8log(1/2*2/3*3/4*4/5)=8log(1/5)