0

Guest

Courses New

dear sir, solve for n;(2n+1)C1 here is: out of 2n+1 objects, 1 object selected. ..and not (2n+1)*C1 (2n+1)C1 + (2n+1)C2 + (2n+1)C3 +....+(2n+1)Cn = 63 [answer ; n=3]

dear sir,


solve for n;(2n+1)C1 here is:out of 2n+1 objects, 1 object selected...and not (2n+1)*C1


(2n+1)C1 + (2n+1)C2 + (2n+1)C3 +....+(2n+1)Cn = 63


[answer ; n=3]

Grade:12

3 Answers

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
14 years ago

Dear H V,

Ans:- Let us consider the expansion (1+X)^(2n+1)

(1+X)^(2n+1)=(2n+1)C0+(2n+1)C1 X +(2N+1)C2 X²+............+(2N+1)C2N X^2N+(2N+1)C(2N+1)X^2N+1................1

Now we know that NCr=NC(N-r)

(2N+1)C1=(2n+1)C2N

(2N+1)C2=(2N+1)C(2N-1)       

Again ,

(2N+1)CN=(2N+1)C(N+1) etc

Hence from these relations we get,(Putting X=1 in eq 1)

2^(2N+1)=(2N+1)C0+2K+(2N+1)C(2N+1)

where K=(2N+1)C1+(2N+1)C2+..............(2N+1)C(2N+1)=63(given)

2^(2N+1)=1+1+126=128

4^N=64=4³

Hence N=3(Ans) 

 

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We
are all IITians and here to help you in your IIT JEE preparation.


All the best H V !!!

 


Regards,

Askiitians Experts
Soumyajit Das IIT Kharagpur

h v
33 Points
13 years ago

can anyone give the answer please?

sunil
13 Points
6 years ago
formula:
(2n+1)C0 +(2n+1)C1+ (2n+1)C2 + (2n+1)C3 +....+(2n+1)Cn=1/2{(2n+1)C0 +(2n+1)C1+ (2n+1)C2 + (2n+1)C3 +....+(2n+1)C2n+1} 
again (2n+1)C0 + (2n+1)C2 + (2n+1)C3 +....+(2n+1)C2n+1= 2^(2n+1)
so (2n+1)C0 +(2n+1)C1+ (2n+1)C2 + (2n+1)C3 +....+(2n+1)Cn=1/2(2^(2n+1))....eq 1
given:
(2n+1)C1 + (2n+1)C2 + (2n+1)C3 +....+(2n+1)Cn = 63
put this in eq1
so (2n+1)C0 +63=1/2(2^(2n+1))
64=1/2(2^(2n+1)) as (2n+1)C0=1
solve this n comes out to be 3

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

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

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

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

Click Here Know More

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

Click Here Know More