Study the monotony of the string xn = 1/(n-1), n>=2.
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
We have xn = 1 / (n-1) and we have to study the monotony for n>=2.
To find the monotony of xn for n>=2, we find the derivative of xn with respect to n
(xn)' = -1/ (n-1)^2
for n>=2, xn' = -1 / (2 - 1)^2 < 0.
Therefore xn is decreasing for all value of n >=2.
Related Questions
- Given the string xn=Sum 1/k(k+1)(k+2) where k = 1 to n , what is xn ?
- 1 Educator Answer
- Prove the induction:...
- 1 Educator Answer
- Calculate the limit n^2/( 1 + 2 + 3 + ... + n ), x->infinity
- 1 Educator Answer
- `1/sqrt(2) + 1/sqrt(3) + 1/sqrt(4) + ... 1/sqrt(n) > sqrt(n), n>= 2` Use mathematical...
- 1 Educator Answer
- Write the first six terms of the sequence given by : a1=a2=1 an=2*an-1 + 3*an-2, n>2 n...
- 2 Educator Answers
To determine if the string, whose general term is xn = 1/(n-1) is increasing or decreasing, we'll have to determine if the difference between 2 consecutive terms of the string is positive or negative.
We'll have to determine xn+1 = 1/(n+1-1)
xn+1 = 1/n
Now, we'll calculate the difference:
xn+1 - xn = 1/n - 1/(n-1)
xn+1 - xn = (n-1-n)/n(n-1)
xn+1 - xn = -1/n(n-1)
Since n>=2, the result of the difference is negative:
-1/n(n-1) < 0 => xn+1 - xn < 0 => xn+1 < xn
The string is strictly decreasing: xn+1 < xn.
Student Answers