Using the principal of mathematical induction prove that 12+14+18+ +12n=1-12n - Maths - Principle of Mathematical Induction

Question

U sin g   t h e   p r i n c i p a l   o f   m a
t h e m a t i c a l   i n d u c t i o n   p r o v e
  t h a t   1 2 + 1 4 + 1 8 + + 1 2 n = 1 - 1 2 n  
                 
                 
                 
                 
                 
    f o r   a l l   n ∈ N

Simranpreet Singh · Answer

Here,
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. U sin g t h e p r i n c i p a l o f m a t h e m a t i c a l i n d u c t i o n p r o v e t h a t 1 2 + 1 4 + 1 8 + . . . + 1 2 n = 1 - 1 2 n f o r a l l n ∈ N

.

$U \sin g t h e p r i n c i p a l o f m a t h e m a t i c a l i n d u c t i o n p r o v e t h a t \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + . . . + \frac{1}{2^{n}} = 1 - \frac{1}{2^{n}} f o r a l l n \in N$