which of the following statements is (are) true for all the positive integers?
1) 2+2^2+2^3+...+ 2^n+2n+1-2
2)1+3+5+...+ n=n^3

Question

which of the following statements is (are) true for all the positive integers?
1) 2+2^2+2^3+...+ 2^n+2n+1-2
2)1+3+5+...+ n=n^3

kinggeorge · Answer

Is there supposed to be an equals sign somewhere in the first one?

anonymous · Answer

2^2=2^n+1-2

kinggeorge · Answer

Should it be $$2+2^2+2^3+...+2^n=2^n+1-2?$$

anonymous · Answer

no here one sec

anonymous · Answer

http://media.education2020.com/EVresources/648-12-09-00-00_files/i0050000.jpg

anonymous · Answer

http://media.education2020.com/EVresources/648-12-09-00-00_files/i0050001.jpg

kinggeorge · Answer

Thanks. Best way to do this, is look at examples. 

Are the following statements true?$$2+2^2=2^3-2$$$$2+2^2+2^3=2^4-1$$

kinggeorge · Answer

The second equation should have a -2 and not -1.

anonymous · Answer

the first ones true and second one isnt.

kinggeorge · Answer

If you take the -2 into account the second equation I wrote is actually true as well. This is a good indication that the overall statement may be true.

anonymous · Answer

ohh well okay thanks man

kinggeorge · Answer

The second statement is easier. Is the following true?$$1+3+5=5^3$$

anonymous · Answer

no false

kinggeorge · Answer

right. So the second statement is definitely false, and the first is probably true.

anonymous · Answer

dopeee i get it know

anonymous · Answer

thanks

kinggeorge · Answer

You're welcome.

anonymous · Answer

they get harder!!