what is an arithmetic progression ? Give examples
Question : what is an arithmetic progression ? Solution : Arithmetic Progression (AP) : Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any…
how to Solve inequality 1-7x ≥ 9-5x
Question : Solve inequality 1-7x ≥ 9-5x. Solution We use to solve an inequality is same as an equation til the last step. 1-7x ≥ 9-5x We shall move -5x…
how to Solve inequality 1-3x ≥ 9-7x.
Question : Solve inequality 1-3x ≥ 9-7x. Solution We use to solve an inequality is same as an equation til the last step. 1-3x ≥ 9-7x We shall move -7x…
how do you solve inequality 52 +8x ≥ 4x +72
Question : Solve inequality 52 +8x ≥ 4x +72 . Solution We solve an inequality is same as an equation til the last step.52 +8x ≥ 4x +72 We shall…
What is power set? give examples
Question : What is power set? give examples Solution: Power set : Let S be a set then power set is the set of all subsets of of S. It…
Prove that 1 + 2 + · · · + n = n(n + 1)/2 for all integers n ≥ 1.
Question: Prove that 1 + 2 + · · · + n = n(n + 1)/2 for all integers n ≥ 1. Proof: We shall prove by induction. Base case:…
Let n be an integer and not divisible by 3 then n^2 = 3k + 1 for some integer k.
Question.: Let n be an integer and not divisible by 3 then n^2 = 3k + 1 for some integer k. Proof: If n is be an integer then n…
Prove that square root of 2 is irrational
Question: Prove that square root of 2 is irrational. Solution: Suppose that √ 2 was rational. By definition of rational numbers √ 2 can be written as a/b for some…
If a b c are in AP then prove that a^2(b+c) b^2(c+a) c^2(a+b) are in AP
Question : If a b c are in AP then prove that a^2(b+c) b^2(c+a) c^2(a+b) are in AP Proof: If a,b,c are in AP \[2b=a+c\] To prove that \[a^2(b+c), b^2(c+a),…
If a b c are in AP then prove that a(1/b+1/c) b(1/c+1/a) c(1/a+1/b) are in AP
Question : If a b c are in AP then prove that a(1/b+1/c) b(1/c+1/a) c(1/a+1/b) are in AP Proof: Given a,b,c are in AP \[2b=a+c \] to prove that \[a(1/b+1/c),…