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Chapter 12: Q 71. (page 809)

In Problems 71鈥�82, find the sum of each sequence.

鈭�k=1405

Short Answer

Expert verified

The sum of this sequence is 200.

Step by step solution

01

Step 1. Write the given information.

The sum of sequence:鈭�k=1405;k=1,...,40

02

Step 2. Use the formula for sum of sequence. 

The formula for summation is:

鈭�ck=1n=c+c+...+c鈬�鈭�ck=1n=cn,c-realnumber

03

Step 3. Use the formula with c=5 and n=40.

Using the formula gives:

鈭�5k=140=5+5+...+5鈬�鈭�5k=140=5脳40鈬�鈭�5k=140=200

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Most popular questions from this chapter

Growth of a Rabbit Colony:

A colony of rabbits begins with one pair of mature rabbits, which will produce a pair of offspring (one male, one female) each month. Assume that all rabbits mature in 1 month and produce a pair of offspring (one male, one female) after 2 months. If no rabbits ever die, how many pairs of mature rabbits are there after 7 months?

[Hint: The Fibonacci sequence models this colony. Do you see why?]

In Problems 17鈥�28, write down the first five terms of each sequence.

bn=nen

In Problems 51鈥�60, write out each sum.

鈭�k=3n-1k+12k

In Problems 61鈥�70, express each sum using summation notation.

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In Problems 51鈥�60, write out each sum.

鈭�k=1nk+2
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