Chapter 12.5, Problem 3CFU

a.

To determine

To determine the number of terms.

Answer to Problem 3CFU

Number of terms are 9.

Explanation of Solution

Given information:

  ${\displaystyle \sum _{j=2}^{10}\left(-2j+1\right)}$

Number of terms can be determined as,

  $N=\left(\text{summation maximum value}\right)-\left(\text{summation maximum value}\right)+1$

Therefore terms are (10-2)+1=9

b.

To determine

To determine the formula for number of terms in finite series.

Answer to Problem 3CFU

Number of terms are $\left(b-a\right)+1$

Explanation of Solution

Given information:

Summation minimum value is $a$ and maximum value is $b.$

Number of terms are given by,

  $N=\left(\text{summation maximum value}\right)-\left(\text{summation maximum value}\right)+1$

Hence number of terms is $\left(b-a\right)+1$

c.

To determine

To determine number of terms.

Answer to Problem 3CFU

There are 6 terms.

Explanation of Solution

Given information:

  ${\displaystyle \sum _{k=-2}^3\frac{1}{k+3}}$

Number of terms are $\left(3-\left(-2\right)\right)+1=6$

d.

To determine

To verify the formula by expanding the series.

Explanation of Solution

  ${\displaystyle \sum _{k=-2}^3\frac{1}{k+3}}=\left(\frac{1}{-2+3}\right)+\left(\frac{1}{-1+3}\right)+\left(\frac{1}{0+3}\right)+\left(\frac{1}{1+3}\right)+\left(\frac{1}{2+3}\right)+\left(\frac{1}{3+3}\right)$

Hence the terms are 6.

Therefore the formula is verified.