Given n(n+1)(2n+1) is divisible by 6 ∀ n ∈ N Proof STEP 1 : We will check if the statement is true for n = 1 n*(n + 1)*(2n + 1) = 1 * (1 + 1) * ( 2*1 + 1 ) = 1 * 2 * 3 = 6 The statement is true …
Prove by mathematical induction n(n+1)(2n+1) is divisible by 6 Read More »
Given If n is not divisible by 3 then n2-1 is divisible by 3 ∀ n ∈ Z Proof For the value of n, we have 3 choices Case 1 : n % 3 = 1 Let, P = (n2-1) % 3 P = ( ( n2 ) % 3 – 1 % 3 ) …
Prove that if n is not divisible by 3 then n^2-1 is divisible by 3 Read More »
Given 2n2 + n + 1 is not divisible by 3 ∀ n ∈ Z Proof We will prove the given statement by direct method. For each value n, we have three choices CASE 1 : n % 3 = 0 S = 2n2 + n + 1 Taking MOD 3 on both sides S …
Prove that if n is an integer then 2n^2+n+1 is not divisible by 3 Read More »
Given If 3n + 2 is odd then n is odd ∀ n ∈ Z Proof By Contradiction We will prove the given statement by contradiction Suppose 3n+2 is odd. Assume n is even. If n is even, then we can write n as n = 2k ∀ k ∈ Z Substitute n in 3n+2 …
Prove that if n is an integer and 3n + 2 is odd then n is odd Read More »
Given If 3n + 2 is even then n is even ∀ n ∈ Z Proof By Contradiction We will prove the given statement by contradiction Suppose 3n+2 is even. Assume n is odd. If n is odd, then we can write n as n = 2k + 1 ∀ k ∈ Z Substitute n …
Prove that if n is an integer and 3n+2 is even then n is even Read More »
Given 1 + 3 + 5 + 7 + ⋯ + (2n-1) = n2 ∀ n ∈ N Proof We will prove the statement using mathematical induction. STEP 1 In this step, we check if the statement is true for n = 1. 1 + 3 + 5 + 7 + ⋯ + (2n-1) = …
Write a program to remove all zeros from a integer number in C/C++. For example, Input 809210003 Output 89213 Steps Take input from the user. Let it be N. Set num = 0. num will store the output. Repeat the following steps while N > 0 Set R = N % 10. This step stores …
Introduction Levenshtein distance between two strings is defined as the minimum number of single-digit edit operations ( Insertion, Deletion, Substitution ) required to convert one string to another. Single Digit Operations Insertion : “Sprk” -> “Spark” Deletion : “Hello” -> “Hllo” Replace : “Carry” -> “Larry” For example, Example 1 s1 = “gone” s2 = …
Given 2n + 1 is divisible by 3 ∀ n ∈ O+ Proof We will prove the given statement by induction. STEP 1 n = 1 2n + 1 = 21 + 1 = 3 3 is divisible by 3. Therefore, the statement is true for n = 1 STEP 2 Let the given statement …
Prove that 2^n + 1 is divisible by 3 for all positive odd integers n Read More »
Given n3 + 2n is divisible by 3 ∀ n ∈ N Proof We will prove the given statement by induction STEP 1 n = 1 n3 + 2n = 13 + 2*1 = 3 3 is divisible by 3. Therefore, the statement is true for n = 1 STEP 2 Let the given statement …
