This PDF 1.7 document has been generated by WPS Office / , and has been sent on pdf-archive.com on 28/08/2017 at 01:39, from IP address 108.218.x.x.
The current document download page has been viewed 157 times.
File size: 28.6 KB (1 page).
Privacy: public file
7. Prove that for any natural number n, 2 + 22 + 23 + ... + 2n = 2n + 1 - 2
Proof by induction.
If n = 1, 2 = 22 - 2. Base case works.
If n = n + 1, 2, 4, 16, ... + 2n + 2n + 1 = 2n + 1 - 2 + 2n + 1
2n + 1 + 2n + 1 - 2 = 2 * 2n + 1 - 2 = 2n + 1 + 1 - 2 = 2n + 2 - 2
The result is 2... + 2n + 2n + 1 = 2n + 1 - 2 + 2n + 1 = 2n + 2 - 2
The theorem holds true as n increases, and so the theorem is true.
proof7.pdf (PDF, 28.6 KB)
Use the permanent link to the download page to share your document on Facebook, Twitter, LinkedIn, or directly with a contact by e-Mail, Messenger, Whatsapp, Line..
Use the short link to share your document on Twitter or by text message (SMS)
Copy the following HTML code to share your document on a Website or Blog