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Prove that 1+2+...+n = n(n+1)/2 for all integers n>0. (Hint: Use induction.)

Let us procede by induction: First case: n=1. Then LHS (left hand side) = 1 and RHS (right hand side) = 1(1+1)/2 = 1. Therefore, we see that the statement is true for n=1. Now, we carry out the inductive ste...
AT
Answered by Aran T. • Maths tutor
4941 Views

Explain the Difference Between a Federal and a Unitary Constitution

Under a unitary constitution, such as the United Kingdom's, decision-making power is centralised in one authority, such as the Westminster parliament. Under a federal constitution, such as the United States'...
MC
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Given that x = ln(sec(2y)) find dy/dx

x = ln (sec (2y)) The chain rule states that d/dy f (g (y)) = f'(g(y)). g'(y) Here g(y) = sec(2y) so g'(y) = 2.sec(2y).tan(2y) And f(y) = ln (y) so f'(y) = 1 / y Thus dx/dy = (1 / sec(2y)) . (2.sec(2y).tan(2...
DH
Answered by Dom H. • Maths tutor
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Perform AND, OR & XOR operations on 0001 1111 & 1010 1010

0001 1111 AND 1010 1010 = 0000 1010 0001 1111 OR 1010 1010 = 1011 1111 0001 1111 XOR 1010 1010 = 1011 0101
DH
Answered by Dom H. • Computing tutor
5459 Views

Create a program that takes in two numbers and returns the highest of the two

print("Enter two numbers. I will tell the highest of the two.") num1 = input("Number 1: ") num2 = input("Number 2: ") if (num1 == num 2) print ("They are the same".) e...
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Answered by Dom H. • Python tutor
2066 Views