1^2 C1+ 2^2 C2+ 3^2 C3+ .........n^2 Cn= ? Answer is n(n+1)2^n-2
Nishi Kaur , 5 Years ago
Grade 12th pass
IIT JEE Entrance Exam> 1^2 C1+ 2^2 C2+ 3^2 C3+ .........n^2 Cn= ...
2 Answers
Arun
Last Activity: 5 Years ago
Dear Nishi
it is∑ r^2 Cr = ∑ r * n (n-1Cr-1)
now n∑ (r-1 +1) (n-1Cr-1)
Now it is easy task
Hope it helps
Aditya Gupta
Last Activity: 5 Years ago
hello nishi, we know that
(1+x)^n= nC0x^0+nC1x^1+nC2x^2+.........+nCnx^n
differentiate wrt x
n(1+x)^(n-1)= nC1 + 2*nC2*x + 3*nC3*x^2 + ….....+ n*nCn*x^(n-1)
multiply both sides by x
nx(1+x)^(n-1)= nC1*x + 2*nC2*x^2 + 3*nC3*x^3 + ….....+ n*nCn*x^n
now differentiate again wrt x
n(x+1)^(n-2)*(nx+1)= nc1+2^2*nC2*x + 3^2*nC3*x^2 + …............ + n^2*nCn*x^(n-1)
now put x= 1 on both sides,
1^2 C1+ 2^2 C2+ 3^2 C3+ .........n^2 Cn= n*2^(n-2)*(n+1)
or n(n+1)*2^(n-2)
kindly approve :)
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on IIT JEE Entrance Exam
My rank is 29k, General, should I opt for any state college cse branch or some Nits in which in which I am getting ECE , chemical, mechanics etc....
IIT JEE Entrance Exam
0 Answer Available
Last Activity: 2 Year ago(s)
How is Ranquer Eduzone,comparing, Akash,Fitjee,Resonance,Naryana
IIT JEE Entrance Exam
0 Answer Available
Last Activity: 2 Year ago(s)
Can class 9th students study syllabus classof 11th
IIT JEE Entrance Exam
3 Answer Available
Last Activity: 2 Year ago(s)
I m foreigner,How much mark i need to get into IIT??
IIT JEE Entrance Exam
1 Answer Available
Last Activity: 2 Year ago(s)