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January 28, 2015

January 28, 2015

Posted by **arzam** on Saturday, November 9, 2013 at 3:06am.

(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+...+(2n-1)

- Math -
**Steve**, Saturday, November 9, 2013 at 5:15amusing 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+...+(2n-1) = n^2

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