Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
259 views
in Binomial Theorem by (49.9k points)
closed by

If the coefficients of (r – 5)th and (2r – 1)th terms in the expansion of (1 + x)34 are equal, find the value of r.

1 Answer

+1 vote
by (55.0k points)
selected by
 
Best answer

To find: the value of r with respect to the binomial expansion of (1 + x)34 where the coefficients of the (r – 5)th and (2r – 1)th terms are equal to each other

Formula Used: The general term, Tr+1 of binomial expansion (x +y)n is given by,

Now, finding the (r – 5)th term, we get

Tr-5 = 34Cr-6 x xr-6

Thus, the coefficient of (r – 5)th term is 34Cr-6

Now, finding the (2r – 1)th term, we get

T2r-1 = 34C2r-2 x (x)2r-2

Thus, coefficient of (2r – 1)th term is 34C2r-2 

As the coefficients are equal, we get

34C2r-2 = 34Cr-6

2r - 2 = r - 6

R = - 4

Value of r = - 4 is not possible 

2r – 2 + r – 6 = 34 

3r = 42 

R = 14 

Thus, value of r is 14

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...