The coefficients of the $(r-1)^{\mathrm{th}}, r^{\mathrm{th}}$ and $(r+1)^{\text {th }}$ terms in the expansion of $(x+1)^{n}$ are in the ratio $1: 3: 5$. Find $n$ and $r$.

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Algebra

NCERT Class 11 - Math

Chapter 8

Binomial Theorem

Section 2

Binomial Theorem for Positive Integral Indices

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Video Transcript

for the coefficient of ar minus one. So is and see ar minus two. And similarly coefficient of art term will be M C R minus one. And the coefficient oh our plus one strong will be and see no the given the issues ah And she ar minus two is two. N C r minus one is two N C R sequence. Okay. Yeah one is to 3 to 5 divide the 1st and 2nd term. We will get N C R minus two form and the ar minus one equals to 1.3. On simplifying the tones we will get and pictorial of corn ar minus two. Pictorial multiplied and minus. Uh huh. That's two factories. Medically ar minus one victorian into and minus R plus one factorial upon. And that story to equal to one of one. Mhm. No simplifying the term. He's really good ar minus one upon and minus R plus two equals one Upon speak. It can be for the simplified two and minus four equals minus of this is our first situation. Now the wait a 2nd and 3rd time we will get and pictorial opponents ar minus one victory in two and minus R plus one. Factorial, multiplied r factorial into n minus r historians. On in victoria he was three upon. No simply fine their terms, we will get three and minus eight. R equals my name is three. This is an immigration number two. No performing another aggression. Yeah. Twice. Oh and minus for R equals two minus state. This is a 30 questions which figured after multiplying the first equation where no subject. Second from third we will get and equals two. Seven substitute an equal to seven. In the second equation, we get the value of art if he goes to Yeah, so the value of and is equal to seven and R equals three will be our final and

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