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Chapter 12: Q 81. (page 809)

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

鈭�k3k=520

Short Answer

Expert verified

The sum of this sequence is 44000.

Step by step solution

01

Step 1. Write the given information.

The sum of sequence:

鈭�k3k=520

02

Step 2. Use the properties of sequence.

Using the properties of sequence:

鈭�k3k=j+1n=鈭�k3k=1n-鈭�k3k=1jSo,鈭�k3k=520=鈭�k3k=120-鈭�k3k=14

03

Step 3. Use the formula for sum of sequences of (n3 ), n - real numbers.

The formula for summation:

鈭�k3k=1n=13+23+...+n3鈬�鈭�k3k=1n=n(n+1)22

So,

鈭�k3k=520=鈭�k3k=120-鈭�k3k=14鈬�鈭�k3k=520=20(20+1)22-4(4+1)22鈬�鈭�k3k=520=10脳212-2脳52鈬�鈭�k3k=520=44100-100鈬�鈭�k3k=520=44000

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Most popular questions from this chapter

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

cn=-1n+1n2

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

鈭�(k2k=014-4)

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

鈭�k=0n-12k+1

In Problems 51鈥�66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

鈭�k=1鈭�813k-1

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

1e+2e2+3e3+.........+nen
See all solutions

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