telescoping series (1 Viewer)

Lith_30

o_o
Joined
Jun 27, 2021
Messages
158
Location
somewhere
Gender
Male
HSC
2022
Uni Grad
2025


tbh I feel like there is a much more nicer way to solve this question, but I guess this method would work.
 

=)(=

Active Member
Joined
Jul 14, 2021
Messages
645
Gender
Male
HSC
2023
I am not quite sure as to the 3 line
 

Lith_30

o_o
Joined
Jun 27, 2021
Messages
158
Location
somewhere
Gender
Male
HSC
2022
Uni Grad
2025
I am not quite sure as to the 3 line
Basically what I am doing is making all the fractions have the same denominator which is

So for example would become by multiplying numerator and denominator by k(k-1).

another example say for the working would be
 

Trebla

Administrator
Administrator
Joined
Feb 16, 2005
Messages
8,114
Gender
Male
HSC
2006
Assuming k is a positive integer, another rather crude way to approach it is to realise that



Notice that



because each factor in the denominator is clearly larger than the numerator, hence the whole denominator is less than the numerator so then



Now notice that each bracketed component on the LHS is positive i.e. for positive integer k



We can then easily argue that



Combining the inequalities, we have the result



Hence, the given inequality holds.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top