Binomial Theorem Cannot Solve: Problems Please Solve it

TOTAL 2 PROBLEMS

It Came in IITJEE 1999

How To Solve This One ?? PLease solve it in DETAIL Stating HOW you got this !

Answer in "nCr" or Factorial Form !!

6 Answers

1
Sonne ·

for q-2 is the answer

2nCn+k ???

\texttt{coefficient of }x^k \texttt{ in the expansion of } \\ \left( 1+\frac{1}{x}\right)^{n}\left(1-x \right)^{n}=\binom{2n}{n+k}

1
Sonne ·

nishant bhaiya , iron man is not having answer with him can u verify if my answer is right ?

62
Lokesh Verma ·

@Sonne... you are correct..

if we see the first question, we should observe that

a and b are straightforward adn there is nothing much to prove there..

If part c is true, then the 4th part follows directly by substituting n = 200

but first look i feel that the sum should be uptil 1/(2n-1) not 1/(2n-1)

341
Hari Shankar ·

Maybe this old thread in goiit will help: http://www.goiit.com/posts/list/algebra-progression-74421.htm

1357
Manish Shankar ·

will read that one when i have tons of tim[3]

6
AKHIL ·

well
i practised problems from TMH for BINOMIAL THEOREM

and the problems were really tuff:(

i m having problem solving these problems!!!

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