Chapter 9.2, Problem 87E

(a)

To determine

To compute the sum of the consecutive positive odd integers.

Explanation of Solution

Consider the following sum of numbers,

  

(b)

To determine

To find the sum of next sequence.

Answer to Problem 87E

The sum of the sequence is-

  

Explanation of Solution

Use the above results, to find the sum of the numbers,

  

(c)

To determine

To verify the conjectures algebraically.

Explanation of Solution

To verify using conjecture the simple method is, to find the sum ofterms of the above sequence, use the formula with value starting from to

Forthe very first term is,

  

Forthe second term is,

  

Forthe third term is,

  

Forthe fourth term is,

  

Forthe fifth term is,

  

Forthe sixth term,

  

Forthe seventh term is,

  

Thus, the above conjecture is verified.