CBSE Class 12-science Answered
mathematical induction problem
Asked by borahbhairabjyoti60 | 20 Mar, 2019, 10:51: PM
Expert Answer
we need to prove 2n > n .................(1)
let n =1 ; then eqn.(1) becomes 2 > 1 , which is true
hence eqn.(1) is true for n =1 ; we need to prove eqn.(1) for any n> 1
let n = k > 1, p(k) = 2k
let us have p(k), 2k > k ................(2)
by multiplying bothe sides of eqn.(2) by 2, 2×2k > 2k or 2k+1 > k+k ................(3)
let k > 1 .............(4)
By adding k to both sides of (4), we have k+k > k+1 ..............(5)
from (3) and (5), we can write , 2k+1 > (k+1) , hence the condition given by eqn.(2) for p(k) also true for p(k+1)
hence by induction, we have , 2n > n for any integer n
Answered by Thiyagarajan K | 21 Mar, 2019, 09:41: AM
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