Chapter ISG, Problem 1.1.1P

a.

To determine

To write an expression

Answer to Problem 1.1.1P

Grey counter= $n^2$

Other counters= $2n+1$

Explanation of Solution

Given information:

Stages of counter

Calculation:

At stage 1,

Grey counter= 1, other counter= 3 (2(1) +1)

At stage 2,

Grey counter= 4, other counter= 5 (2(2) +1)

At stage 3,

Grey counter= 9, other counter=7 (2(3) +1)

Observing the pattern,

At stage n,

Grey counter= $n^2$ and other counters will be $2n+1$

b.

To determine

To write 2 different expression

Answer to Problem 1.1.1P

  ${(n+1)}^2$ And $n^2+2n+1$

Explanation of Solution

Given information:

Stages of counter

Calculation:

Grey counter= $n^2$ and other counters will be $n^2+2n+1$

Total number of counters= grey counter + other counter

Substituting values,

Total counters = $n^2+2n+1$

This is the first expression.

2^nd expression:

Total values= ${(n+1)}^2$

Hence, both expressions are correct as one expression is an expanded form of other expression.

  ${(n+1)}^2$ = $n^2+2n+1$ .