What is the first part of the second step to prove that Sn 1 + 2 + 4 +. + 2n - 1 = 2n - 1? a. Show that Sn is valid for n = k c. Assume that Sn is valid for n = k b. Verify that Sn is valid for n = 1 d. Prove that Sn is valid for n = k + 1

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02-05-2022
Mathematics

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What is the first part of the second step to prove that Sn 1 + 2 + 4 +. + 2n - 1 = 2n - 1? a. Show that Sn is valid for n = k c. Assume that Sn is valid for n = k b. Verify that Sn is valid for n = 1 d. Prove that Sn is valid for n = k + 1

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 1 · 2022-05-13T03:33:39+02:00

The first part of the second step to prove the sequence is to prove that Sn is valid for n = k + 1, Option D is correct.

What is geometric sequence?

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

The sum of geometric sequence is given as,

[tex]s_n=\dfrac{r^n-1}{r-1}[/tex]

Here, a is the first term of the sequence, n is total terms and r is the common ratio.

The given equation which need to be proved is,

[tex]S_n= 1 + 2 + 4 +. ...+ 2n - 1 = 2n - 1[/tex]

This can be proved by induction method. This can be done by induction method with two steps:

Prove n=0, without getting any data of other cases.
If the data or problem is given then assume n=k.
For the given case is also true for n=k+1. Thus, in second step prove that Sn is vaild for n=k+1.

Thus, the first part of the second step to prove the sequence is to prove that Sn is valid for n = k + 1, Option D is correct.

Learn more about the geometric sequence here;

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