prove that 2n is greater than n for all positive integers n.

this is example 2 from the ncert maths text book.

plzz...answer soon....i dint get the last step.

using the principle of mathematical iduction.

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P(n)=2n>n

Let it is true for n=1

21>1

Therefore it is true for n=1

Let it is true for n=k

2k>k

Multiply both sides by 2,

2k.2>2k

=> 2k+1>k+k>k+1 (2k=k+k, Also k+k is always greater than k+1 which ultimately induces that 2k+1 is greater than k+1)

Therefore it is true for n=k+1

Hence By Principle of Mathematical induction , P(n) is true for all n belongs to N.

Hope it helps!!

Cheers!!

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cheers !!!! XD
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k+k is not greater than k+1 for k=1
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K+k is not greater than k+1 for k=0,1
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you have done a short mistake "trunaya". you have done wrong in the following step. i hope it will not be done by u again.  
  2 power (k+1)  >  2k 
 2 power ( k+1 ) > k + k 
 2 power ( k+ 1) > k+ k > or equal to k+ 1 
 2 power  ( k+ 1) > k + 1    { because k+ k > or equal to k + 1 } 
Don't worry. Following is the derivation of the {k + k > or equal to  k + 1 } 
let k = 1 
therefore, k + k  > or equal to k+ 1 
1 + 1  > or equal to k + 1 
2 > or equal to 1 + 1 
2 = 2 
hence k = 1 is true for k+ k = k +  1 
now, we have to prove that  k + k  > k + 1 
let, k = 2 
k + k > k + 1 
2 + 2 > 2 + 1  
4  > 3 
hence it is also true for k + k > k + 1 
so we can say that  k + k > or equal  to k+ 1 
so from this it is proved that 
2 power (k+ 1 ) >  k + 1 
hence, by principle of mathematival induction p(n) is true for all n epsillon (or belongs to) N 
                               ( hope like my suggestion if like then convert likes into thousands i would motivate to upload many solutions of your queries as soon as possible ) thanks 
 
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