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CBSE Class 11-science Answered

mathematical induction problem
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Asked by borahbhairabjyoti60 | 21 Mar, 2019, 11:45: AM
answered-by-expert Expert Answer
let us assume for k>4,  we have  k! > 2k  ..................(1)
 
by multiplying both sides of eqn.(1),  (k+1) × (  k! )  >  (k+1) × 2k  ........................(2)
 
LHS of eqn.(2) is  ( k+1 )! , hence we have (k+1)! >  (k+1) × 2k  ........................(3)
 
let us consider , 2k+1 = 2k × 2    if  k > 2, then (k+1) × 2k  > 2×2k   or  (k+1) × 2k  > 2k+1  ................(4)
 
from (3)  and (4),  we have (k+1)! > 2k+1  ..................(5)
 
hence by induction, it is proved that  n! > 2n  for n > 4
Answered by Thiyagarajan K | 21 Mar, 2019, 01:08: PM

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