Question

prove :
log (n+1) - log n > 3/(10n)

Answer 1

Use this on LHS:

\[\large Log(a) - Log(b) = Log(\frac{a}{b})\]

Answer 2

looks tough

Answer 3

y i see.. but i stuck in next step :(

Answer 4

is that a prove :
or solve ?

Answer 5

prove, not solve

Answer 6

may be you can try induction method

Answer 7

how to use it??

Answer 8

yu know the induction principle used in+1????

Answer 9

when the formula is true ,you should use the method of mathematical proof,assuming that formula is true when 'n'.then prove it is true when 'n+1'.

Answer 10

firstly proving the result is true for n=1
then assuming it true for n=k,any positive integer
then to prove it true for n=k+1 using the result for n=k

Answer 11

for n=1,
log 2 > 3/10
0.301... > 0.3 (right)
for n=k,
=> log((k+1)/k)) > 3/(10k) (assuming it true)
for n=k+1,
=> log((k+2)/(k+1)) > 3/(10k+10)
what is the next step??

Answer 12

i told you using kth one,we have to prove for n=k+1
so replace k with k+1 in
log(k+1/k)>3/10k,,,,,,,,,and the result is there

Answer 13

since it is true for any positive integer k+1 ,,,,,,,,,it is true for all n>0

Answer 14

got it???????

Answer 15

sorii i cant prove for n=k+1, help me please..

Answer 16

n is positive integer?

Answer 17

not rule that n must be positive integer...
i think from log (n+1), then n+1>0 or
n>-1, maybe...