71+ pages prove that n 3 2n is divisible by 3 5mb. For any positive integer n prove that n3 - n is divisible by 6Welcome to Doubtnut. So find the difference and then simplify it and then consider how to prove its divisible by 3. N22 becomes 9k26k3 which is divisible by 3. Check also: divisible and learn more manual guide in prove that n 3 2n is divisible by 3 If n is not multiple of 3 then n22 must be divisible by 3.
Now we need to prove. Thus if n is a multiple of 3 then it is divisible by 3.
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N can take values 3k1 or 3k2 where k is an integer.
Basis StepThe statement P1 is true because 1310 is divisible by 3. From 1 and 2 a must be divisible by 2 3 6 Thus n n is divisible by 6 for any positive integer n. Use mathematical induction to prove that n 3 n is divisible by 3 whenever n is a positive integer. From the above cases we can conclude that If n is not divisible by 3 then n 2 -1 is divisible by 3 n Z. We will prove the given statement by induction. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy Safety How YouTube works Test new features Press Copyright Contact us Creators.
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P n 3 n 3 2 3. Basis StepThe statement P1 is true because 1310 is divisible by 3. Let the given statement be true for n k.
Here is all you need to learn about prove that n 3 2n is divisible by 3 P n 3 n 3 2 3. Use Mathematical Induction to prove that n3-n is divisible by 3 whenever n is positive integer. N 3 2. Cbse 2013 2014 class 11 half yearly question papers maths question paper maths paper math math jokes physics memes math a visual proof that 10 11 12 13 14 chrome extension home library plex hyperbolic trigonometry proofs sin iz isinh z and sinh iz math word problems framed words math journals integral of sqrt u math videos math udemy a visual proof that 10 11 12 13 14 chrome extension home library Therefore the statement is true for n 1.
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