Asked by Lia
How many terms of the series the summation from n equals 1 to infinity of the quotient of negative 1 raised to the n plus 1 power and n do we need to add in order to find the sum with an absolute value of its error to be less than 0.05? (4 points)
A) 20
B) 15
C) 17
D) The series diverges so no sum is possible.
A) 20
B) 15
C) 17
D) The series diverges so no sum is possible.
Answers
Answered by
oobleck
ever think of actually writing the math?
sum(n=1..infinity) (-1)^(n+1)/n
or even better,
∑(n=1..∞) (-1)^(n+1)/n
You know that if S_n = ∑(-1)^n a_n then
|S - Sn| < a_(n+1)
so you just need n such that
1/(n+1) < 1/20
n+1 > 20
n > 19
Check:
∑k=1..n for n= 18,19,20 is
0.6661398
0.7187714
0.6687714
S∞ = log2 = 0.69315
you can read online about the alternating harmonic series
sum(n=1..infinity) (-1)^(n+1)/n
or even better,
∑(n=1..∞) (-1)^(n+1)/n
You know that if S_n = ∑(-1)^n a_n then
|S - Sn| < a_(n+1)
so you just need n such that
1/(n+1) < 1/20
n+1 > 20
n > 19
Check:
∑k=1..n for n= 18,19,20 is
0.6661398
0.7187714
0.6687714
S∞ = log2 = 0.69315
you can read online about the alternating harmonic series
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.