Question

Prove that the sum of 2 consecutive integers is positive

Answer #1

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Using PMI prove that the sum of the first n positive odd
integers is n2?
Is there a way to prove it substituting n+1 for n in the LHS and
RHS?

find three consecutive integers with a sum of the first and third
equal the sum of 1.5

1.The three sides of a triangle are consecutive even integers.
If the perimeter (sum of the three sides) of the triangle is 318
feet, find the length of each side of the triangle.
2.The three sides of a triangle are consecutive integers. If the
perimeter (sum of the three sides) of the triangle is 486 yards,
find the length of each side of the triangle.

Five consecutive positive integers , p, q, r,s,t, each less than
10,000, produce a sum which is a perfect square, while the sum q+ r
+ s is a perfect cube. What is the value of the square root of
p+q+r+s+t ?

Using pigeonhole principle prove that in any group of 5
integers, not necessarily consecutive, there are 2 with same
remainder when divided by 9

prove that the sum of two odd integers is even

Prove deductively that for any three consecutive odd integers,
one of them is divisible by 3

The
left and right page numbers of an open book are two consecutive
integers whose sum is 405. Find these page numbers.

one of your curious students noted the following interesting
relationship; when she added 2 consecutive odd integers, teh sum
was divisible by 2. when she added 3 consecutive odd integers the
sum was divisible by 3. she made the conjecture that the sum of n
consecutive odd numbers is divisible by n. is she correct? how
would you help her prove or disprove her conjecture

Using induction prove that for all positive integers n, n^2−n is
even.

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