Question

m and n are natural no's such that m + n = 2014, then find the value of (-1)^m + (-1)^n is __,__

Answer 1

⇰ Given

• m and n are natural numbers such that m + n = 2014

⇰ To find

• (-1)ᵐ + (-1)ⁿ

⇰ Solution

⇾ We shall take two cases, if m and n are even and m and n are odd.

➛ If m and n are even :

• (-1)ᵉᵛᵉⁿ + (-1)ᵉᵛᵉⁿ = 1 + 1
• 2

⇾ ∴ If m and n are even, the value is 2

⟶ Ex : (-1)² + (-1)⁴

          : 1 + 1

          : 2

➛ If m and n are odd :

• (-1)ᵒᵈᵈ + (-1)ᵒᵈᵈ = - 1 - 1
• -2

⇾ ∴ If m and n are even, the value is -2

⟶ Ex : (-1)³ + (-1)⁵

          : - 1 - 1

          : -2

∅ ∴ If m and n are natural numbers such that m + n = 2014, then the value of (-1)ᵐ + (-1)ⁿ is 2 and -2

⇾ Always remember

• - × - = +
• + × + = +
• - × + = -
• + × - = -

➛ - is minus (subtraction)

➛ + is plus (addition)

➛ × is multiply (multiplication)