Question

I need help with this question.

(Computer Algorithms)

10. (10 %) Use proof by mathematical induction to show that N +1

Answer 1

for = 1

1(1 2 0.5

RHS 11 2 0.5

let' s assume LHS-RHS forn k

ng that Σ_ï_ i(i + 1) so, assuming that k+1

so, for N- k+1

$LHS=\sum_{i=1}^{k+1}\frac{1}{i(i+1)}$

$=\frac{1}{(k+1)(k+2)}+\sum_{i=1}^{k}\frac{1}{i(i+1)}$

$=\frac{1}{(k+1)(k+2)}+\frac{k}{k+1}$

k(k 2)

A2k1

$=\frac{(k+1)^2}{(k+1)(k+2)}$

k + 2

.V に! 1) N+1