Alternating Series: Intervals
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can you take a look at the link below where I uploaded a math problem solved by my professor. In part d), how did he arrive to -0.234? The -0.242 is 0.008 + that 0.234, but both intervals are negative. Both interval numbers have confused me, I'd appreciate it if someone could clarify. I would ask him but it's the weekend and I need to understand before I proceed with the problem.
Thank you!
calculus
edited Nov 17 at 16:19
José Carlos Santos
142k20112208
asked Nov 17 at 16:13
RochNoure
134
add a comment |
up vote
1
down vote
favorite
can you take a look at the link below where I uploaded a math problem solved by my professor. In part d), how did he arrive to -0.234? The -0.242 is 0.008 + that 0.234, but both intervals are negative. Both interval numbers have confused me, I'd appreciate it if someone could clarify. I would ask him but it's the weekend and I need to understand before I proceed with the problem.
Thank you!
calculus
edited Nov 17 at 16:19
José Carlos Santos
142k20112208
asked Nov 17 at 16:13
RochNoure
134
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
can you take a look at the link below where I uploaded a math problem solved by my professor. In part d), how did he arrive to -0.234? The -0.242 is 0.008 + that 0.234, but both intervals are negative. Both interval numbers have confused me, I'd appreciate it if someone could clarify. I would ask him but it's the weekend and I need to understand before I proceed with the problem.
Thank you!
calculus
edited Nov 17 at 16:19
José Carlos Santos
142k20112208
asked Nov 17 at 16:13
RochNoure
134
can you take a look at the link below where I uploaded a math problem solved by my professor. In part d), how did he arrive to -0.234? The -0.242 is 0.008 + that 0.234, but both intervals are negative. Both interval numbers have confused me, I'd appreciate it if someone could clarify. I would ask him but it's the weekend and I need to understand before I proceed with the problem.
Thank you!
calculus
calculus
edited Nov 17 at 16:19
José Carlos Santos
142k20112208
asked Nov 17 at 16:13
RochNoure
134
edited Nov 17 at 16:19
José Carlos Santos
142k20112208
asked Nov 17 at 16:13
RochNoure
134
edited Nov 17 at 16:19
José Carlos Santos
142k20112208
edited Nov 17 at 16:19
José Carlos Santos
142k20112208
edited Nov 17 at 16:19
José Carlos Santos
142k20112208
142k20112208
asked Nov 17 at 16:13
RochNoure
134
asked Nov 17 at 16:13
RochNoure
134
asked Nov 17 at 16:13
RochNoure
134
134
add a comment |
add a comment |
1 Answer
1
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votes
up vote
1
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accepted
We are evaluating the sum up to the first 10 terms and we obtain $-0.2346$ since the next term is negative we are over estimating the sum and the lower bound is obtained adding the $11^{th}$ term which leads to $-0.2421$.
The key fact is that the upper sum (even terms) is decreasing and the lower sum (odd terms) is increasing that is for any $n$
$$S_{2}le S_{4} le ldots le S_{2n}le S_{infty} le S_{2n-1} le ldots le S_{3}le S_{1}$$
answered Nov 17 at 16:26
gimusi
88.7k74394
Got it. Thank you both!!
– RochNoure
Nov 17 at 16:55
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
We are evaluating the sum up to the first 10 terms and we obtain $-0.2346$ since the next term is negative we are over estimating the sum and the lower bound is obtained adding the $11^{th}$ term which leads to $-0.2421$.
The key fact is that the upper sum (even terms) is decreasing and the lower sum (odd terms) is increasing that is for any $n$
$$S_{2}le S_{4} le ldots le S_{2n}le S_{infty} le S_{2n-1} le ldots le S_{3}le S_{1}$$
answered Nov 17 at 16:26
gimusi
88.7k74394
Got it. Thank you both!!
– RochNoure
Nov 17 at 16:55
add a comment |
up vote
1
down vote
accepted
We are evaluating the sum up to the first 10 terms and we obtain $-0.2346$ since the next term is negative we are over estimating the sum and the lower bound is obtained adding the $11^{th}$ term which leads to $-0.2421$.
The key fact is that the upper sum (even terms) is decreasing and the lower sum (odd terms) is increasing that is for any $n$
$$S_{2}le S_{4} le ldots le S_{2n}le S_{infty} le S_{2n-1} le ldots le S_{3}le S_{1}$$
answered Nov 17 at 16:26
gimusi
88.7k74394
Got it. Thank you both!!
– RochNoure
Nov 17 at 16:55
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
We are evaluating the sum up to the first 10 terms and we obtain $-0.2346$ since the next term is negative we are over estimating the sum and the lower bound is obtained adding the $11^{th}$ term which leads to $-0.2421$.
The key fact is that the upper sum (even terms) is decreasing and the lower sum (odd terms) is increasing that is for any $n$
$$S_{2}le S_{4} le ldots le S_{2n}le S_{infty} le S_{2n-1} le ldots le S_{3}le S_{1}$$
answered Nov 17 at 16:26
gimusi
88.7k74394
We are evaluating the sum up to the first 10 terms and we obtain $-0.2346$ since the next term is negative we are over estimating the sum and the lower bound is obtained adding the $11^{th}$ term which leads to $-0.2421$.
The key fact is that the upper sum (even terms) is decreasing and the lower sum (odd terms) is increasing that is for any $n$
$$S_{2}le S_{4} le ldots le S_{2n}le S_{infty} le S_{2n-1} le ldots le S_{3}le S_{1}$$
answered Nov 17 at 16:26
gimusi
88.7k74394
edited Nov 17 at 16:44
answered Nov 17 at 16:26
gimusi
88.7k74394
answered Nov 17 at 16:26
gimusi
88.7k74394
answered Nov 17 at 16:26
gimusi
88.7k74394
88.7k74394
Got it. Thank you both!!
– RochNoure
Nov 17 at 16:55
add a comment |
Got it. Thank you both!!
– RochNoure
Nov 17 at 16:55
Got it. Thank you both!!
– RochNoure
Nov 17 at 16:55
Got it. Thank you both!!
– RochNoure
Nov 17 at 16:55
add a comment |
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