Please solve the problem from binomial theorem. 1) Find the coefficient of x^65 in the expansion of x(x+1)^2(x+2)^3(x+3)^4.........(x+10)^11 2). Find the coefficient of x^(n^2+n-14)/2 in the expansion of (x-1)(x^2-2)(x^3 -3).........(x^n-n)

Question

Aditya Gupta · Answer

Roots of x(x+1)^2...(x+10)^11 are 0, -1, -1, -2, -2, -2,..., -10, -10,...,-10 Also, the degree of the above polynomial is 1+2+...+11= 66. So coefficient of x^65 is the following sum: ∑r(r+1), r ranging from 0 to 10. This is because of viettas formulas taking the roots one at a time. The above sum is easy to find coz ∑r^2 and ∑r already have standard formulas

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

Please solve the problem from binomial theorem. 1) Find the coefficient of x^65 in the expansion of x(x+1)^2(x+2)^3(x+3)^4.........(x+10)^11 2). Find the coefficient of x^(n^2+n-14)/2 in the expansion of (x-1)(x^2-2)(x^3 -3).........(x^n-n)

Please solve the problem from binomial theorem.
1) Find the coefficient of x^65 in the expansion of x(x+1)^2(x+2)^3(x+3)^4.........(x+10)^11
2). Find the coefficient of x^(n^2+n-14)/2 in the expansion of (x-1)(x^2-2)(x^3 -3).........(x^n-n)

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

IIT JEE Courses

One Year IIT Programme

Two Year IIT Programme

Crash Course

NEET Courses

One Year NEET Programme

Two Year NEET Programme

One to One

School Board

Live Online classes

Class 11 & 12

Class 9 & 10

Class 6, 7 & 8

Test Series

JEE test series

NEET test series

C.B.S.E test series

Complete Self Study Packages

FULL COURSE

For class 12th

For class 11th

Please solve the problem from binomial theorem. 1) Find the coefficient of x^65 in the expansion of x(x+1)^2(x+2)^3(x+3)^4.........(x+10)^11 2). Find the coefficient of x^(n^2+n-14)/2 in the expansion of (x-1)(x^2-2)(x^3 -3).........(x^n-n)

Please solve the problem from binomial theorem.1) Find the coefficient of x^65 in the expansion of x(x+1)^2(x+2)^3(x+3)^4.........(x+10)^112). Find the coefficient of x^(n^2+n-14)/2 in the expansion of (x-1)(x^2-2)(x^3 -3).........(x^n-n)

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Please solve the problem from binomial theorem.
1) Find the coefficient of x^65 in the expansion of x(x+1)^2(x+2)^3(x+3)^4.........(x+10)^11
2). Find the coefficient of x^(n^2+n-14)/2 in the expansion of (x-1)(x^2-2)(x^3 -3).........(x^n-n)