If the coefficients of x7 and x8 in (2+3x)n are equal, then n is

Coefficient of T8=T9Then, nC7.2n−7.3−7=nC82n−8.3−8nC7.2.3=nC8(n−7)!.7!6.n!=(n−8)!.8!n!6(8)=n−7∴n=55

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

If the coefficients of x^7 and x^8 in (2+ {x}{3} )^n are equ

Question

If the coefficients of $x^{7}$ and $x^{8}$ in $(2 + \frac{x}{3})^{n}$ are equal, then $n$ is

Views: 674 students

Found 7 tutors discussing this question

Emma Discussed

If the coefficients of

x^{7}

and

x^{8}

(2 + \frac{x}{3})^{n}

are equal, then

n

5 mins ago

Discuss this question LIVE

5 mins ago

Coefficient of

T_{8} = T_{9}

Then,

^{n} C_{7} . 2^{n - 7} . 3^{- 7} =^{n} C_{8} 2^{n - 8} . 3^{- 8}

^{n} C_{7} .2.3 =^{n} C_{8}

\frac{6. n !}{( n - 7 )! .7 !} = \frac{n !}{( n - 8 )! .8 !}

6 (8) = n - 7

∴ n = 55

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	If the coefficients of $x^{7}$ and $x^{8}$ in $(2 + \frac{x}{3})^{n}$ are equal, then $n$ is
Answer Type	Text solution:1
Upvotes	150