It is proved by mathematical induction that 32n + 2-8n-9 (n ∈ n) can be divisible by 64

It is proved by mathematical induction that 32n + 2-8n-9 (n ∈ n) can be divisible by 64

Proving binomial theorem
It is known that in the expansion of (1 + x) ^ n, the sum of odd items is a, and the sum of even items is B. to prove that a ^ 2-B ^ = (1-x ^ 2) ^ n requires detailed steps

(1-x^2)=(1+x)(1-x)
(1-x^2)^n=(1+x)^n*(1-x)^n
Where (1 + x) ^ n = a + B, (1-x) ^ n = a-b
Note: (1 + x) ^ n, (1-x) ^ n have the same odd number terms, but the even number terms are opposite to each other
So (1-x ^ 2) ^ n = (1-x) ^ n * (1 + x) ^ n = (a + b) * (a-b) = a ^ 2-B ^ 2

Urgent: a high school proof about binomial theorem
Verification: 2 < = (1 + 1 / N) ^ n

Method 1: [you are required to have a good mathematical foundation]
Let f (x) = (1 + 1 / x) ^ x, find the derivative, and get f (x) increasing at [1, infinity]
When f (1) = 2 LIM (1 + 1 / x) ^ x tends to infinity, e = 2.7