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For someone struggling with learning the expansion.. just understand the taylor series or maclaurin series, all the expansion could easily be derived from there. Anyways nice questions, struggled a bit but did it 👍
For the last problem which you mentioned 1/(3n)! It is quiet easy, just put 1, w, and w² in the expansion of (e)^x and add all the three series you directly get, the required ans. In addition to this for finding the summation of any integral mutiple of a number like for example, you want to find 1/(5n)! Then, put the roots of 5th root of unity one by one in (e)^x and add all of them, theough this i think we will be able to find for any nth multiple of n.
@@Colded-h1m yes, and as we know that sum of nth roots of unity is zero, so the unwanted terms each have coefficient of sum of nth roots of unity which will be zero, and hence we would be left with only the required ones.
Bhaiya aab aap tagada explanation krr rhe ho ! ITF wale session me Accha samjate to the but Iss level pe nahi ! TYSM abhi sabh acche se samaj aaraha hai
Bhaiya 3rd question karte samay I finally reached to 1/3 (Σ[1/(n-3)!]) Limit n = 0 to ∞, but how can this be possible, negative number aa jayega inside factorial I considered 1/(n-2)! inside the sigma, am I wrong?
@@soumilmittal9874 okay uska ek solution hota hai Jaise suppose Σ(n/n!) , n = 0 to ∞ Agar (n-1)! me leke jana hai to aaise Karo n = 0 wala term sum ke bahar taaki (n-1)! me n = 0 na ho sake i.e 0 + Σn/n(n-1)! , here n = 1 to ∞ = Σ1/(n-1)!, n = 1 to ∞ = e Aaise lekin 3rd question me aaisa nhi kar sakte
@mathsshikshajee for n³/n! Write e^X expansion = 1+x/1!+x²/2! +...... Differentiate it e^x= 1/1!+2x/2!+3X²/3!+..... Now multiply with X Xe^x= x + 2X²/2!+3X³/3!+..... Differentiate it Do it same again and see magic Differentiate it
@@mathsshikshajee bro e^x differentiation is still e^x .... I think avi 10th ya 11 th me honge it's ok ekbr dekh lena Xe^x differentiation is e^x+ Xe^x
Revision start ni kiya hoga?
Enrolments are now open for revC25, Only 60 entries open for live program! courses.jeesimplified.com/courses/Revision-Course-Math-and-Physics-66ec38402c79b06466a55fe8-66ec38402c79b06466a55fe8
For someone struggling with learning the expansion.. just understand the taylor series or maclaurin series, all the expansion could easily be derived from there.
Anyways nice questions, struggled a bit but did it 👍
For the last problem which you mentioned 1/(3n)!
It is quiet easy, just put 1, w, and w² in the expansion of (e)^x and add all the three series you directly get, the required ans.
In addition to this for finding the summation of any integral mutiple of a number like for example, you want to find 1/(5n)! Then, put the roots of 5th root of unity one by one in (e)^x and add all of them, theough this i think we will be able to find for any nth multiple of n.
@@FAUXVIKINGIITB For any gap of k terms putting kth terms of unity and adding kth equations gives f(a)+f(ka)+..
Do u have the answers to other 2 ques?
@@Colded-h1m yes, and as we know that sum of nth roots of unity is zero, so the unwanted terms each have coefficient of sum of nth roots of unity which will be zero, and hence we would be left with only the required ones.
2024 me ayega sun sun k mujhe lagne laga tha mai pichhle saal ka video dekh raha 😅
Bhaiya aab aap tagada explanation krr rhe ho ! ITF wale session me Accha samjate to the but Iss level pe nahi ! TYSM abhi sabh acche se samaj aaraha hai
I do remember solving something like this in limits not revising killed my math
Solved 2 from the 3 questions, and i already knew the actual concept.
Do u have the answers to other 2 ques?
People who did this after knowing that no v(n) methd is used❤
please also share the final answers for the other 2 questions .... thank you!
Bhaiya 3rd question karte samay I finally reached to 1/3 (Σ[1/(n-3)!])
Limit n = 0 to ∞, but how can this be possible, negative number aa jayega inside factorial
I considered 1/(n-2)! inside the sigma, am I wrong?
Same mera bi aesa hi sum aaya hai
Same bro i did something else but having the same problem. Negative number in factorial
@@soumilmittal9874 okay uska ek solution hota hai
Jaise suppose Σ(n/n!) , n = 0 to ∞
Agar (n-1)! me leke jana hai to aaise Karo n = 0 wala term sum ke bahar taaki (n-1)! me n = 0 na ho sake
i.e
0 + Σn/n(n-1)! , here n = 1 to ∞
= Σ1/(n-1)!, n = 1 to ∞
= e
Aaise lekin 3rd question me aaisa nhi kar sakte
@@ExquisiteHappiness ok bro tysm!!🙏🙏
@@ExquisiteHappiness do u have the ans for other 2 ques?
Differentiation of ex multiplying with x two times and done
can u explain or give source?
@mathsshikshajee for n³/n!
Write e^X expansion = 1+x/1!+x²/2! +......
Differentiate it
e^x= 1/1!+2x/2!+3X²/3!+.....
Now multiply with X
Xe^x= x + 2X²/2!+3X³/3!+.....
Differentiate it
Do it same again and see magic
Differentiate it
@@JitakaharKalita sounds fabulous, but while differentiating e^x become x.e^(x-1) ?? But you didn't
@@mathsshikshajee bro e^x differentiation is still e^x .... I think avi 10th ya 11 th me honge it's ok ekbr dekh lena
Xe^x differentiation is
e^x+ Xe^x
@@JitakaharKalita ok i knew that but i forgot , i am in 11 th . thanks for guiding 👍
Ye saare important expansion ki ek lec bana do pls
Bros comment section is flooded with air
whats the answer for rest two??
Answers of rest two?
Bhaiya pls reply
I am confused
I want a book for theory and tough illustrations
So i am confused btw arihant and om sharma pls reply
Om sharma
Cengage
Pw module ofc
Blackbook
@@Mjmaths-x4k theory achi nhi hai om mei
Lagta hai pichle year ka video edit krke daal diya😂
Yesb khudse figure out krne me kitna mehnat laga tha bhaiya ap free me competition badha rahe ho🗣️😩
Which chapter problem is this
In my opinion differentiation is just easier
how can it be done thru differentiation?
@vijaysingh-vx4gf use the Taylor series expansion of e^x and differentate using binomial theorem method
Okay thanks bro
Do u have the answers to other 2 ques?
If NTA actually sticks to syllabus this time then Summation of series is out of syllabus
very subtle
2nd and third hogye but first waala nahi horaha, koi please bta sakta hai.
thank god easy vala tareeka reveal nhi hua
@@shivx3295 🤔🤔🤔🤔🤔
kya h easy walaa tareeka??
What is the easy method?
maza aagaya
Sir plz provide the correct ans for the other 2!!!😢 not able to find it anywhere
2024 nhi 2025
@@shivx3295 yes😅
First ! Pin plss