Series and Proof

∑r from r=1 to n

∑r from r=1 to n

0.5n(n+1)

steps in proof by induction

basis, assumption, inductive, conclusion

how to prove by induction summations of a series with terms f(r) up to n

• ∑ up to (k+1) = ∑ up to k + (k+1)th term

• replace ∑ up to k with the given expression

• rearrange to make the given expression with (k+1)

how to prove by induction divisibility of the expression f(n) by m

f(k+1)= λf(k) + mx