On the problem of quadratic term theorem, (1) If today is Monday and today is counted as the first day, what day is the 19th power of the 8th? (2) In (1 + x) n times = 1 + a1x + a2x +... + an-1xn-1 times + anxn times, if 2a4 = 3an-6, then the value of n is (3) Given that the ratio of the coefficients of two adjacent terms in the expansion of degree (1 + x) n is 8:15, then the minimum value of n is to explain how 8 (n-k) = 15 (K + 1) comes out

On the problem of quadratic term theorem, (1) If today is Monday and today is counted as the first day, what day is the 19th power of the 8th? (2) In (1 + x) n times = 1 + a1x + a2x +... + an-1xn-1 times + anxn times, if 2a4 = 3an-6, then the value of n is (3) Given that the ratio of the coefficients of two adjacent terms in the expansion of degree (1 + x) n is 8:15, then the minimum value of n is to explain how 8 (n-k) = 15 (K + 1) comes out

(1) If today is Monday and today is counted as the first day, what day is the 19th power of the 8th?
(2) In (1 + x) n times = 1 + a1x + a2x +... + an-1xn-1 times + anxn times, if 2a4 = 3an-6, then the value of n is 9
(3) Given that the ratio of the coefficients of two adjacent terms in the expansion of degree (1 + x) n is 8:15, then the minimum value of n is 22. Explain how 8 (n-k) = 15 (K + 1) comes out
Help write down the derivation process, quadratic theorem
(a+b)n＝Cn0an+Cn1an-1b1+… +Cnran-rbr+… +Cnnbn(n∈N*)
This formula is called binomial theorem. The polynomial on the right is called the quadratic expansion of (a + b) n, where the coefficient CNR (r = 0,1,...) n) It is called the coefficient of quadratic term, cnran RBR in the formula. It is called the general term of binomial expansion, which is expressed by tr + 1, that is, the general term is the R + 1 term of the expansion: tr + 1 = cnraa RBR
It is shown that (1) tr + 1 = cnraa RBR is the R + 1 term of the expansion of (a + b) n. r = 0,1,2 n. It is different from cnrbn rar, the R + 1 term of the expansion of (B + a) n
② TR + 1 only refers to the standard form of (a + b) n. The general formula of binomial expansion of (a-b) n is tr + 1 = (- 1) rcnran RBR
③ The coefficient CNR is called the binomial coefficient of the R + 1 degree of the expansion, which should be distinguished from the coefficient of the R + 1 term with respect to one or more letters
In particular, in the binomial theorem, if a = 1, B = x, then we get the formula:
(1+x)n＝1+cn1x+Cn2x2+… +Cnrxa+… +xn.
When n is a small positive integer, we can use Yang Hui triangle to write the corresponding coefficients