Series and Proof

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∑r from r=1 to n

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0.5n(n+1)

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steps in proof by induction

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basis, assumption, inductive, conclusion

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4 Terms

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∑r from r=1 to n

0.5n(n+1)

2
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steps in proof by induction

basis, assumption, inductive, conclusion

3
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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)
4
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how to prove by induction divisibility of the expression f(n) by m

f(k+1)= λf(k) + mx