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Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)

Base case - First let us consider the base case where n=1. Then the left hand side of the equation becomes 1 and the right hand side is (1/6)12*3=6/6=1. Thus LHS=RHS and we are d...

AR
5863 Views

Expand (x+4)(x-4)=33 to give values of x

Use FOIL to expand the brackets. To do this, we start by multiplying the FIRST value in each bracket which in this case is x so we get x^2. Then we multiply the OUTSIDE two values, so here that is x and -...

AB
Answered by Aria B. Maths tutor
3594 Views

How do surds relate to powers and roots?

To understand surds we have to understand powers and there uses. So to start we should look at powers such as what is 22 , 32, and 52. This shows us going up but then we l...

AG
Answered by Alistair G. Maths tutor
3213 Views

Describe the structure and function of a chloroplast

Chloroplasts are organelles found only in plants that allow the plant to release energy from sunlight through photosynthesis. They are green in colour because they contain the pigment chlorophyll.

JB
Answered by Joy B. Biology tutor
5067 Views

Explain why an athlete loses water when exercising.

The athlete begins to sweat, as exercising releases energy from the body in the form of heat, so the water evaporating from the surface of the skin results in the body cooling down.

JB
Answered by Joy B. Biology tutor
2699 Views

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