- #1
Daaniyaal
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1. Homework Statement [/b]
Use mathematical induction to prove the following statements are true for all integers n≥1
1+2+2^2+2^3+...+2^n-1=2^n-1
Attempt at a solution:
For n=1
1+2^(1-1)=2^1-1
1=1
∴ it is true.
Let Sn=Sk
If it is true for k, it must also be true for k+1
1+2+2^2+2^3+...+2^k+2^k+1-1=(2^k+1)-1
This is the part I have a slight confusion at, I keep getting something left over and the sides don't equal each other :(
Use mathematical induction to prove the following statements are true for all integers n≥1
1+2+2^2+2^3+...+2^n-1=2^n-1
Attempt at a solution:
For n=1
1+2^(1-1)=2^1-1
1=1
∴ it is true.
Let Sn=Sk
If it is true for k, it must also be true for k+1
1+2+2^2+2^3+...+2^k+2^k+1-1=(2^k+1)-1
This is the part I have a slight confusion at, I keep getting something left over and the sides don't equal each other :(