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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
4947 Views

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
13694 Views

Solve the equation x^2 - 8x + 5 = 0 by completing the square

x 2 - 8x + 5 = 0 => (x 2 - 8x + 16) - 11 = 0 =>(x - 4) 2 = 11 =>x - 4 = +- sqrt(11) =>x = 4 +- sqrt(11)
DH
Answered by Dom H. • Maths tutor
4039 Views

Vectors

k=3
JS
Answered by Joshua S. • Maths tutor
3723 Views

Solve these simultaneous equations, 2x+y=6 and 3y-x=11

First step is to choose between the three methods for solving simulataneous equations; elimination, substitution and eqaulity. In this case the best method is probably substitution, but personal preference i...
EG
Answered by Edward G. • Maths tutor
5705 Views