
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
January 29th, 2019, 11:43 AM  #1 
Senior Member Joined: Dec 2015 From: iPhone Posts: 387 Thanks: 61  Series sum proof
How to prove it or disprove it? Is it true? $\displaystyle \sum_{j=1}^{\infty} \lfloor \frac{n}{2^j }\rfloor=n+1 \; $, $\displaystyle n,j \in \mathbb{N}$. Last edited by skipjack; January 30th, 2019 at 12:18 AM. 
January 29th, 2019, 12:07 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,314 Thanks: 1230 
Your questions are all over the map. Can I ask what exactly you ask them for? They don't seem to be related to a few classes. Are you a tutor getting answers here? I would be fine with that if you were up front about it. 
January 29th, 2019, 12:22 PM  #3 
Senior Member Joined: Dec 2015 From: iPhone Posts: 387 Thanks: 61 
Something about odd and even numbers. Got it by inspection; it is not true. Last edited by skipjack; January 30th, 2019 at 12:18 AM. 
January 29th, 2019, 07:57 PM  #4 
Senior Member Joined: Sep 2016 From: USA Posts: 559 Thanks: 324 Math Focus: Dynamical systems, analytic function theory, numerics  Take $n = 1$, then for all $j \in \mathbb{N}$ you have $\frac{n}{2^j} < 1$ so the sum on the left hand side is equal to 0.
Last edited by skipjack; January 30th, 2019 at 12:20 AM. 

Tags 
proof, series, sum 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Proof that a series is divergent  WWRtelescoping  Complex Analysis  2  March 27th, 2014 01:08 AM 
Proof of divergence for the harmonic series  SlamDunk  Algebra  11  April 18th, 2012 12:21 PM 
proof of x^1 as a power series  geordief  Calculus  2  January 8th, 2012 09:27 AM 
Proof of the series expansion of log(x)  Weiler  Calculus  10  January 2nd, 2012 07:00 PM 
Proof series using differentiation  wnvl  Calculus  4  November 25th, 2011 01:44 PM 