A level further maths : prrof by induction and summation

What is the formula for the sum of all infringers from 1 to n

What is the formula for the sum of all squares from 1 to n

What is the formula for sum of the cubes from 1 to n

What are the three marking points for all proof by induction questions ?

True for n=1

True for n=k then true for n=k+1

so true for all positive I tiger values of n by mathematical induction

What should you consider when having an inequality in a summation question

That the answer must be greater than or equal to one

How to complete a divisibility proof by induction question ?

1, consider f(k+1)-f(k)

2.write all coefficients in terms of f(k) by manipulating the powers

3. Simplify the terms

4. Divide the coefficients into a+b in order to take a factor of the divided number out