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July 31, 2014

July 31, 2014

Posted by **Brock** on Wednesday, August 8, 2012 at 3:31pm.

1. 1 + 2 +…+n = n(n+1)/2

2. 1/1*2 + 1/2*3+…+1/n*(n+1) = n/n+1

- Calculus -
**Steve**, Wednesday, August 8, 2012 at 3:46pmfor k=1, 1 = 1(2)/2

hyp: as shown

1+...+ k + (k+1) = k(k+1)/2 + (k+1)

= [k(k+1) + 2(k+1)]/2

= (k+1)(k+2)/2

for k=1, 1/1*2 = 1/2

1/1*2 + ... + 1/k(k+1) + 1/(k+1)(k+2)

= k/(k+1) + 1/(k+1)(k+2)

= (k(k+2) + 1)/(k+1)(k+2)

= (k+1)^2 / (k+1)(k+2)

= (k+1)/(k+2)

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