My Calculus 2 Exam#3 Solution (sequence & series)

Thanks to Vibing math for the time stamps:
0:00 hello
Q1 3:00 Sum 3(-1/4)^(n-1)
Q2 4:10 Check Absolute Convergent for 4 series
Q3 9:26 Sum (-1)^n/(n^2 x 3^n), Radius of convergence
Q4 14:00, Want Limit a_n=0, but sum of a_n divergent
Q5 17:50, Power series for 5x^2/(4-x) with R and I
Q6 22:44, 1/3+1/6+1/9+1/12+...
Q7 24:50, 2/1-4/2+8/6-16/24+32/120-..Determine Conv or Div & explain
Q8a 31:28, Integrate as power series, ln(1+3x)/x
Q8b 38:54, Integrate sin(x^2)
Q9 44:54, Sum (cos(1/n))^3 conv or div?
Q10 48:33, a. Your favourite sequence, b. Your favourite series
Q11 52:40, Sum 1/(n sqrt(1+ln n)) conv or div?
Q12 59:28, 1/8, 1/15, 1/24, 1/35, ..... a. Does a_n conv? b. Does Sum a_n conv?
Q13 1:06:20, Find 3rd degree Taylor polynomial for cosx at x=π/4

[AthyXrayGD]

Time stamps for questions:
#1: 2:57
#2: 4:12
#3: 9:33
#4: 13:59
#5: 17:52
#6: 22:44
#7: 24:47
#8 a: 31:28
#8 b: 38:49
#9: 44:53
#10 a: 48:31
#10 b: 50:35
#11: 52:41
#12 a: 59:25
#12 b: 1:01:40
#13: 1:06:15

[blackpenredpen]

Can anyone help me with the time stamp for the 13 question? I will appreciate it very much and your comment will be hearted and pinned.

[VibingMath]

Here you are man and thank you for your effort again. Good luck to your students and stay safe!

1:10:58 Power of trio

Q1 3:00
Sum 3(-1/4)^(n-1)

Q2 4:10
Check Absolute Convergent for 4 series

Q3 9:26
Sum (-1)^n/(n^2 x 3^n)
Radius of convergence

Q4 14:00
Want Limit a_n=0, but sum of a_n divergent

Q5 17:50
Power series for 5x^2/(4-x) with R and I

Q6 22:44
1/3+1/6+1/9+1/12+...

Q7 24:50
2/1-4/2+8/6-16/24+32/120-..
Determine Conv or Div & explain

Q8a 31:28
Integrate as power series
ln(1+3x)/x

Q8b 38:54
Integrate sin(x^2)

Q9 44:54
Sum (cos(1/n))^3 conv or div?

Q10 48:33
a. Your favourite sequence
b. Your favourite series

Q11 52:40
Sum 1/(n sqrt(1+ln n)) conv or div?

Q12 59:28
1/8, 1/15, 1/24, 1/35,
a. Does a_n conv?
b. Does Sum a_n conv?

Q13 1:06:20
Find 3rd degree Taylor polynomial for cosx at x=π/4

[Peter_]

First time I have seen Pikachu in a challenging math video.

I really like when math enthusiasts add a playful and charming spin to math.

[MathemaTeach]

Wow!!! New mic. I love it... its soo cute. Summation nitation for geometric series is my lesson today in my Integrated Math 3 class and we are doing it online too, that is how i came up with my you tube channel to get my lesson up there. Good job!!! 👍👍👍👍

[JSSTyger]

Calc 2 for me was integration. Calc 1 was limits and derivatives. Calc 3 was series and sequences. Calc 4 was double and triple integrals and use of polar coordinates.

[fnlfdctfgtdg]

AP calc BC exam is tommorow. I'm grateful for all the calc videos on this cannel. Thank you bprp, very cool! Wish me luck!

[julianmejiac]

33:56 For 8a) Before doing the computations we can first make the u-substitution u=3x, so your integrand becomes ln(1+u)/u du. You don't have to deal with the powers of 3 at all, just don't forget to replace u=3x at the very end.

[drewpatterson]

Professor, can you help me. I am still confused with Q3. I know you are using a formula for the radius of convergence, but using the ratio test should still work too. When I use the ratio test, I get that (5/3)<x<(7/3). Why does this method not work here?

[MuPrimeMath]

The Powerful Trio will be the first to solve the Riemann hypothesis

[brianoq]

"how it looks" or "what it looks like"
But either way, math looks awesome any day

[abhirupchakraborty]

Sir how to send you queries? I requested you to find the Fourier sine and cosine transformations of the function {cosh(ax)/sinh(πx)} previously on a comment. But you didn't replied. Please help me to find the answer. I shall be highly obliged..

With love and best wishes,
A regular viewer and admirer of your channel

[andresgomes]

por favor me podria ayudar con la integral definida, de 0 hasta 1, de ((1-x^2)^1/2)ln(1-x/1+x)

[muckamuckamojo]

For the first problem he does: number 3, isn’t the formula a/(1-r) supposed to be used for a summation starting from n=0? So the correct answer should be (12/5) - whatever partial sum you get plugging in n=0? Please correct me if I’m wrong

[giovannimariotte]

Exams are comin. You should do a doble and triple integrals marathon

[brtsevin]

Oh my god a video I didn't watch at the end. Thank you .

[Dalton]

I learned how to find the sum of an infinite geometric series when I took algebra 2/trigonometry in the 11th grade, and I remember the formula to use in order to find the sum if the series converges

[Observer]

I think i love you too much. Any tips for an A-level student sir. If i send you an A-level paper can you do it for me. Pure maths?

[lucaschai]

Pikachu现在又比小兔兔厉害吗?.BTW, blackpenredpen，你是什么人， 是台湾人吗，还是外星人？YAY, I AM THE FIRST

[GhostyOcean]

I got most of them right, but a few had simple transcribing mistakes. I think I finished in 20 minutes? Probably could've checked my answers and fixed the typos if I weren't rushing to finish the exam b4 the stream ended (joined about 35 minutes in)