唔該幫我解呢題數，係A.maths

Let P (n) be the proposition (n+1)(n+2)(n+3).......(n+n) = 2n．1．3．5......(2n-1)

When n = 1,

L.H.S. = 1 + 1 = 2

R.H.S. = 21 = 2 = L.H.S.

Therefore P (1) is true.

Assume P ( k ) is true for some positive integers k.

i.e. (k+1)(k+2)(k+3).......(k+k) = 2k．1．3．5......(2k - 1)

When n = k + 1 ,

L.H.S. = (k+1+1)(k+2+1)(k+3+1).......(2k+ 2 – 2)(2k+ 2 – 1)( 2k + 2 )

= ( k + 1 )( k + 2 )( k + 3 )( k + 4 )……(2k)(2k+ 1)(2)

= 2k．1．3．5......(2k+1)(2)

= 2k+1．1．3．5......(2k+1)

R.H.S. = 2k．1．3．5......(2k+2-1)

= 2k+1．1．3．5......(2k+1)

= L.H.S.

Therefore P ( k + 1 ) is true.

By the principle of mathematical induction, P ( n ) is true for all positive integers n.