Use mathematical induction to prove the following.  . . .  = 

What will be an ideal response?

Answers may vary. One possibility:
Sn:    . . .  = 
S1:   = 
Sk:    . . .  = 
Sk+1:    . . .    = 
1. Basis step: Since  =  = 1 - , S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
  . . .  = 
  . . .    =   
 =   
 =   
 =   
 = .

Mathematics

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