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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 :(