Q2.7 Please include a formal proof. Thanks! a for all n E N. 2. Prove that 1/2 + 1/4 + 1/8 + ... + 1/2" = 1 - 1/2" for all n E N. "/> Prove each of the following using induction: 1. Let a E R and a >...

Q2.7

Please include a formal proof. Thanks!

a for all n E N. 2. Prove that 1/2 + 1/4 + 1/8 + ... + 1/2" = 1 - 1/2" for all n E N. "/>
Extracted text: Prove each of the following using induction: 1. Let a E R and a > 1. Prove a" > a for all n E N. 2. Prove that 1/2 + 1/4 + 1/8 + ... + 1/2" = 1 - 1/2" for all n E N.