Sum of Geometric Series Proof by Induction

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Last updated 8:22 PM on 4/12/26
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7 Terms

1
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To prove

Sn = a+ ar + ar2+ ar3 + ……. arn-1 = a(1-rn)/1-r

2
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First term is

a

3
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Step 1

Show true for n = 1

4
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Step 2

Assume true for n = k

5
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Step 3

Prove true for n = k + 1

6
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How to show true for n = 1

S1 = a(1-r1)/1-r , S1 = a

∴ True for n = 1

7
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How to assume true for n = k

a+ ar + ar2 + ……. a rk-1 = arn-1 = a(1-rk)/1-r

∴ True for n = k