數學歸納法可不可以從RHS做到LHS ?

數學歸納法可不可以從RHS做到LHS ?

先看看aCb + aCb-1
我是證實了aCb + aCb-1 = a+1Cb --(1)

(n)S(r->0) - (nCr)[x^(n-r)](y^r)

S (nCr)[x^(n-r)](y^r) = (x+y)^n

* S(1) is true
Assume S(k) is true and
when n = k+1

(x+y)^(k+1)
(x+y)^k * (x+y)
x [x^k + kC1 x^(k-1)(y) + ....] + y [x^k + kC1 x^k-1(y) + ....]

x^(k+1) + kC1 x^k y + ... +
x^k(y) + kC1 x^k-1(y)^2 + ....

Put x^k(y) = kC0 x^k(y)

kC1 x^k y + kC0 x^k(y) ..........
From (1) ,
kC1 x^k y + kC0 x^k(y) = k+1 C1 x^k(y)

Therefore ,

x^(k+1) + kC1 x^k y + ... +
x^k(y) + kC1 x^k-1(y)^2 + ....

= x^(k+1) + k+1C1 x^k(y) + k+1C2 x^(k-1)(y^2) + ....
=LHS

請問我這樣做可以嗎?