Math
1.(A)(i)Show that 2+4+6+8+..+2n=n(n+1).
(ii)Find the sum of the first 200 even numbers.
(iii)Find the sum of the first 200 odd numbers.
(B)(i)Use the formula at the beginning of the question to find the sum of the first 2n natural numbers.
(ii)Find a formula, in its simplest form, for 1+3+5+7+9+...+(2n1)
asked by
arzam

using induction
if n=1, 2 = 1(2) = 2
assuming true for n=k,
check for n=k+1:
2+...+2k+2k+2
= k(k+1) + 2k+2
= k(k+1) + 2(k+1)
= (k+1)(k+2)
as desired.
1+3+5+...+(2n1) = n^2posted by Steve
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