What a coincidence! I too used the telescopic series and the idea of general term to solve this. At last I also got 1/2! - 1/2024!, this seemed not good to me as I felt it may be a vague answer but anyway, I continued with your video. I'm happy at last that I got one of the answers to be right after solving many of the questions from your thumbnail and video!
I'm going to have to watch this again. Summations with the signa notation were always a puzzle for me as was probability with permutations and combinations.
An interesting aside: the general term of the related INFINITE series looks very similar to the general term for the Maclaurin series for e¹ - the difference is the "k+2" in the denominator. A way to get that in the denominator is to multiply the series for e^x by x: x + x²/1! + x³/2! + x⁴/3! + ... Integrate that term by term one gets the series you have here with x = 1 and an extra term in front of 1/2 that comes one term in front of x²/2. To sum the series then you can integrate xe^x from 0 to 1 and subtract 1/2; the series sum is 1 so you get 1/2 for the sum of the infinite series - as it should since the limit of the tiny correction is 0 when you let 2024 → ∞.
@@PrimeNewtons You missed the chance to showcase your hat by posing so that the summation sign that you put in the forefront of the screen would be perfectly aligned on the top part of your hat. I also like that hat, and it is good enough to get a brief 5 seconds when it is the star of the show :)
Didn't know what I was looking at... Written it as sum 1/((n+2)n!) and guessed 1/2 from first 4 terms, which is hella close, considering I don't do maths very often
I’m confused about the 5:47 to 6:20 minute mark. How do you go from (k+1)! to (k+1)k! and how do you go from (k+2)! to (k+2)(k+1)k!? Can someone explain the steps in doing that?
Thanks brother you are just amazing!! ..one question speaking about "series" on the "Soul-Series" what are your believes..do you believe in the Lord JesusChrist?
It's beautiful to see how the telescoping series saved the day. Thank you, you are an amazing teacher
What a coincidence! I too used the telescopic series and the idea of general term to solve this. At last I also got 1/2! - 1/2024!, this seemed not good to me as I felt it may be a vague answer but anyway, I continued with your video. I'm happy at last that I got one of the answers to be right after solving many of the questions from your thumbnail and video!
You are a Great Teacher
Thank you from Hong-Kong (but I am french...)! Your explanations are always clear and accuratr, I enjoy every time!
Glad you like them!
Telescoping series. Very interesting. Thanks.
I'm going to have to watch this again. Summations with the signa notation were always a puzzle for me as was probability with permutations and combinations.
Excellent sir❤ . I appreciate your approach. Your teaching method is so easy that we can understand very easily
Wow got it in first try !! Thank you sir for such beautiful questions ....love your videos ❤
Great idea!
An interesting aside: the general term of the related INFINITE series looks very similar to the general term for the Maclaurin series for e¹ - the difference is the "k+2" in the denominator. A way to get that in the denominator is to multiply the series for e^x by x: x + x²/1! + x³/2! + x⁴/3! + ... Integrate that term by term one gets the series you have here with x = 1 and an extra term in front of 1/2 that comes one term in front of x²/2. To sum the series then you can integrate xe^x from 0 to 1 and subtract 1/2; the series sum is 1 so you get 1/2 for the sum of the infinite series - as it should since the limit of the tiny correction is 0 when you let 2024 → ∞.
Never see telecoping series. But I would whatch a video about them. Greate work
Good 👍
Thank you for this problem, it was very fun to solve :D
Awesome. Thanks.
Beautiful!
12:40 That's scary😈
🤣🤣🤣
Got a new hat? Looks great 😀
Not new. Just not frequently worn compared to others .
@@PrimeNewtons You missed the chance to showcase your hat by posing so that the summation sign that you put in the forefront of the screen would be perfectly aligned on the top part of your hat. I also like that hat, and it is good enough to get a brief 5 seconds when it is the star of the show :)
@@Jon60987 🤣🤣🤣🤣🤣
Telescopic series ✨
面白い～😄
Didn't know what I was looking at... Written it as sum 1/((n+2)n!) and guessed 1/2 from first 4 terms, which is hella close, considering I don't do maths very often
Nice problem
👍👍👍👍
I’m confused about the 5:47 to 6:20 minute mark. How do you go from (k+1)! to (k+1)k! and how do you go from (k+2)! to (k+2)(k+1)k!? Can someone explain the steps in doing that?
Nevermind, I figured it out.
Oh! I get it now! Yay! Go Prime Newtons!
I am currently struggling to figure out why P.N. did not do the formula from 1 and then subtract of the easy bits at the start...
"...a very small number..."
Yep. Unless you're looking for an answer with over 5800 significant digits, the answer is 0.5...
answer is: 1/2 - 1,5479244899×10⁻⁵⁸¹⁵ just a little very little bit less than 0.5 😄
What sort of people dream up these questions at the first place.
next video: calculate 2024! manually 😂
🤣🤣
This series converges to 1/2.
Double beauty
Thanks brother you are just amazing!! ..one question speaking about "series" on the "Soul-Series" what are your believes..do you believe in the Lord JesusChrist?
Simple. Just whip out your calculator. lol NO! I want to see how Prime Newtons does it.
Esplendido.