# Calculus

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.

1. 👍
2. 👎
3. 👁
1. 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

1. 👍
2. 👎

## Similar Questions

1. ### Algebra 2

Use summation notation to write the series 2+4+6+8 for 10 term in each of these images, the lower limit of the summation notation is either n=1, or n=0

2. ### Math

Write the limit as n goes to infinity of the summation from k equals 1 of the product of the 10th power of the quantity 5 plus 2 times k over n and 2 over n as a definite integral.

3. ### Calculus

Which of the following statements is true for the series the summation from n=0 to infinity of (-1)^n and 5/4^n? a) The series diverges because it is geometric with r = 5/4 and a = –1. b) The series converges to 4 because it is

4. ### Calculus

Which one of the following statements is true about the series the series from n equals 1 to infinity of the quotient of negative 1 raised to the nth power and n ? (4 points) Is this A or B? I am a little confused. A) It is

1. ### Calculus

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 is convergent. Use the Alternating Series Test to find an upper bound on the absolute error if the 7th partial

2. ### Calculus

Use the nth term test for divergence to determine which, if any, of the following infinite series diverge(s). (10 points) I got D ( OR all of them ), did I do this right? I. the summation from n equals 1 to infinity of the nth

3. ### Quick calc question

The Riemann sum, the limit as the maximum of delta x sub i goes to infinity of the summation from i equals 1 to n of f of the quantity x star sub i times delta x sub i , is equivalent to the limit as n goes to infinity of the

4. ### Calculus

Match each series to the test that should be used to test for convergence/divergence. While it is possible that each test could apply to more than one series, in this exercise each is only used once. (4 points) 1. the summation

1. ### ALGEBRA

USE SUMMATION NOTATION TO WRITE A ARITHMETIC SERIES FOR THESE TERMS. PLEASE SHOW HOW TO DO IT. 15+25+35+...; N=7 4+8+12+...; N=4 3+7+11+...;N=8

2. ### Calculus

Find the derivative of the summation from n equals 0 to infinity of the quotient of the product of negative 1 raised to the nth power and x raised to the quantity 2 times n plus 1 power and the product of 3 to the 2 times n power

3. ### calculus

f(x) = summation from n equals 0 to infinity of the quotient of the quantity n plus 1 and 3 to the n plus 1 power times x to the nth power with an interval of convergence, –3 < x < 3. Find exactly the value of the integral from

4. ### Calculus

Write the limit as n goes to infinity of the summation from k equals 1 of the product of the 4th power of the quantity negative 1 plus 3 times k over n and 3 over n as a definite integral.