which of the following is true statement ?
a. a finite series has no sum
b. any finite series has a sum
c. some infinite arithmetic series have a sum
d. all infinite arithmetic series have a sum
So the answer is A ?
since arithmetic series have a constant difference, they cannot have a finite sum. The differences have to get smaller and smaller for that to happen.
So, what do you think?
sigh
Nope. B -- you are adding a finite number of values. of course it has a sum!
Which of the following statements is true?
a. Any infinite series has a sum
b. A series has no sum if it is finite
c. An infinite arithmetic series has sum.
d. Not all infinite geometric series has sum.
Well, isn't this a series of interesting options!? Let me break it down for you with a dash of humor.
a. a finite series has no sum - Oh, come on! Imagine you have a bowl of ice cream with a limited number of scoops. Of course, it has a sum. It's just a matter of spooning it all together.
b. any finite series has a sum - Now we're talking! Yes, any finite series, just like a collection of cute little pandas, can be summed up. So don't worry, all those numbers can find their happy ending.
c. some infinite arithmetic series have a sum - How do you explain this one? Well, it's like an all-you-can-eat buffet, but sometimes the chefs forget to refill the food trays. So, yeah, some infinite series have a sum, while others are just left unfinished plates.
d. all infinite arithmetic series have a sum - Ah, the never-ending story! Unfortunately, not all infinite arithmetic series come with a neat sum. It's like expecting a clown car to fit an infinite number of clowns. Eventually, someone is going to be left standing outside, wondering why they don't fit.
So, my friend, the correct answer is c. Some infinite arithmetic series have a sum. Just like life, it's a mix of possible and impossible sums. Enjoy the mathematical circus!
To determine which statement is true, let's analyze each option:
a. A finite series has no sum.
This statement is false. A finite series, by definition, is a series that has a limited number of terms. As long as the terms have a defined pattern or rule, a finite series can indeed have a sum. For example, the series 1 + 2 + 3 + 4 has a sum of 10.
b. Any finite series has a sum.
This statement is true. As mentioned earlier, a finite series is a series with a limited number of terms. As long as the terms of the series can be added, the series will have a sum. This includes arithmetic, geometric, and other types of series.
c. Some infinite arithmetic series have a sum.
This statement is true. An infinite arithmetic series is a series with an unlimited number of terms, but it can still have a sum if certain conditions are met. For example, the series 1 + 2 + 3 + 4 + ... does not have a sum because it grows infinitely. However, the series 1 + 3 + 5 + 7 + ... (where each term increases by 2) does have a sum of infinity.
d. All infinite arithmetic series have a sum.
This statement is false. While some infinite arithmetic series have a sum, not all of them do. If the terms of an infinite arithmetic series have a pattern or rule that causes the series to grow infinitely, the series will not have a finite sum.
In summary, the correct answer is:
c. Some infinite arithmetic series have a sum.