In the binomial (2^1/3+3^-1/3)^n ,if the ratio of the 7th term from the beginning of the expansion to the 7 - Maths - Mathematical Induction and Binomial Theorem

Question

In the binomial (2^1/3+3^-1/3)^n ,if the ratio of the 7th term from
the beginning of the expansion to the 7 term from its and is 1/ 6
then n is equal to

Manbar Singh · Accepted Answer

In the expansion of 23 + 133n, n+1-7+1th i
e
 n-5th term from the beginning is7th term from the end
Now, T7 = C6n 23n-6 × 1336=C6n × 2n3-2 ×32Now, Tn-5 = Cn-6n × 236 × 133n-6=C6n × 22× 13n3-2Now, T7Tn-5 = 16⇒C6n × 2n3-2 ×32C6n × 22× 13n3-2 = 16⇒164 - n3 = 161⇒4 - n3 = 1⇒n3 = 3⇒n = 9

In the binomial (2^1/3+3^-1/3)^n ,if the ratio of the 7th term from the beginning of the expansion to the 7 term from its and is 1/ 6 then n is equal to