PLEASE SHOW WORK & EXPLAIN 1 1 1-2 2-3 Here is a general outline you can use. 1.

Question

PLEASE SHOW WORK & EXPLAIN

1 1 1-2 2-3 Here is a general outline you can use. 1. Basis step. Prove P(1) 2. Induction step a. Write out P(k) by replacing n" with k" in the original equation. b. Now replace ink" with "k+1." This is what we need to show. c. Using the assumption that P(k) is true, replace "1+2+... +k" in the P(k+1) statement. d. If necessary, multiply away any constant denominators in the new POk+1) formulation e. Multiply out the left-hand side and the right-handside to establish the equality

Explanation / Answer

a) P(1) LHS = 1/2

RHS = 1/2

b)1/1.2 +1/2.3.....1/k(k+1) = 1.k/(k+1)

putting k = k+1

1/1.2 +1/2.3.....1/k+1(k+2)

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

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

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

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

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

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

=p(K+1)

RHS

hence proved

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