use mathematical induction to prove the statement is true for all positive integers n. 6 + 12 + 18 + ... + 6n = 3n(n + 1)​

Step-by-step explanation:

6+12+18+6n=3n(n+1)

Proof by induction

True for n = 1

6 = 3(1)(1+1)

Assume true for n = k

6+12+18+6k=3k(k+1)

Then show that

6+12+18+6(k+1)= 3(k+1)(k+1+1)

We add 6(k+1) to both sides of

6+12+18+6k=3k(k+1)

6+12+18+6k +6(k+1) =3k(k+1) + 6(k+1)

= 3(k+1)(k + 2)

= 3(k+1)(k+1+1)

So true for n = k+1

Since true for n=1 it is true for n=2,3,...

Thus true for all natural numbers n by mathematical induction

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify