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Use mathematical induction to prove the statement is true for all positive integers n.
10 + 20 + 30 + ... + 10n = 5n(n + 1)

Answer :

chi3fcomm5nd
to prove something by induction you need to verify 2 things
1-the base case,2-it holds for n+1
the base case n=1
10=5(1)(1+1) which is true
it holds for n+1
10+20+30+....+10(n+1)=5(n+1)(n+2)
5n(n+1)+10(n+1)=5(n+1)(n+2)
(5n+10)(n+1)=5(n+1)(n+2)
5(n+2)(n+1)=5(n+1)(n+2) which is true our proof is done.

Using Mathematical Induction, we have been able to prove that the given statement is true for all positive integers n.

How to carry out Mathematical Induction?

We are given the mathematical statement;

10 + 20 + 30 + ... + 10n = 5n(n + 1)

Let us first test if the given mathematical statement holds true for n = 1. Thus;

10 = 5(1)(1 + 1)

When solved, right hand side is also 10 and so it is true for n = 1

Let us now test if it holds true for n + 1;

10 + 20 + 30 + .... + 10(n + 1) = 5(n + 1)(n + 2)

From earlier, we have;

5n(n + 1) + 10(n + 1)

Collecting factored terms gives;

(5n + 10)(n + 1)

This can be factored again to get;

5(n + 2)(n + 1)

This result is equal to the right hand side for  (n + 1) and so by mathematical induction, the statement holds true.

Read more about Mathematical Induction at; https://brainly.com/question/24672369

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