Use induction to show that 12 + 22 + 32 + + n2 = n(n+1)(2n+1)/6, for all n > 1.

Answer with Step-by-step explanation:

Let

Substitute n=2

Then  

Hence, P(n) is true for n=2

Suppose that P(n) is true for n=k >1

Now, we shall prove that p(n) is true for n=k+1

LHS

Substitute the value of P(k)

LHS=RHS

Hence, P(n) is true for all n >1.

Hence, proved

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v