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Suppose Sn is defined as 2 + 22 + 23 + . . . + 2n . What is the next step in your proof of Sn = 2(2n - 1), after you verify that Sn is valid for n = 1?
 A. Show that Sn is valid for n = k + 2.
B. Assume that Sn is valid for n = k .
C. Verify that Sn is valid for n = 1.
D. Show that Sn is valid for n = k.

Respuesta :

Remark:

[tex]S_n=2*1+2*2+2*3+...+2*n=2(1+2+3+...+n)[/tex]

[tex]1+2+3+...+n= \frac{n(n+1)}{2} [/tex], by the famous Gauss formula.

So the formula for [tex]S_n[/tex] is:

[tex]S_n=2*\frac{n(n+1)}{2}=n(n+1)[/tex]



these types of formulas are proven by Induction.

The first step is proving for n=1,

then the next step is assuming Sn is valid for n=k.



Answer: B. Assume that Sn is valid for n = k .

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