Proving $1 + 2 + 2^2+2^3 + 2^4 + \dots+ 2^{n-1}= 2^n -1$ using mathematical induction

Asked Apr 23 '20 at 19:42

Active Apr 23 '20 at 20:07

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I'm taking Pre-Calc, and if anyone could go through step-by-step on this problem I’d appreciate it greatly. ;)

Use mathematical induction to prove the formula for every positive integer n.

$$1 + 2 + 2^2+2^3 + 2^4 + \dots+ 2^{n-1}= 2^n -1$$

edited Jun 12 '20 at 10:38

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asked Apr 23 '20 at 19:42

Sabir Aden

1

This question has, undoubtedly, been asked many times on this site. – Andrew Chin Apr 23 '20 at 19:44
Really? I’m new to the site – Sabir Aden Apr 23 '20 at 19:45
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Can you see why the case $n=1$ works? Can you see why if $n=k$ works so does $n=k+1$? – J.G. Apr 23 '20 at 19:46
How you simplify 2^(k) -1 + 2^k – Sabir Aden Apr 23 '20 at 19:53

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