Prove That:

2^n<3^n

Asked by jgjaigupta1998 | 15th May, 2014, 01:07: PM

Expert Answer:

G i v e n : space  space space space space space space space space space space space space 2 to the power of n space less than space 3 to the power of n  n equals 1  space 2 space less than space 3 space space space t r u e  L e t s space a s s u m e space t h e space g i v e n space i n e q u a l i t y space i s space t r u e space f o r space n equals k comma space t h e n  space space space space 2 to the power of k space less than space 3 to the power of k space space space space space... space left parenthesis i right parenthesis  N o w comma space space f o r space n equals k plus 1  space 2 to the power of k plus 1 end exponent space comma space space space 3 to the power of k plus 1 end exponent space  rightwards double arrow 2.2 to the power of k space comma space 3.3 to the power of k  rightwards double arrow 2.2 to the power of k space end exponent less than space space 3.3 to the power of k space space space space space w h i c h space i s space t r u e space f o r space n space equals space k plus 1  T h e r e f o r e comma space t h e space g i v e n space i n e q u a l i t y space h o l d s space t r u e.

Answered by Avinash Soni | 15th May, 2014, 01:47: PM

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