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Chapter 1: 4P (page 17)

In the following problems, find the limit of the given sequence asn鈫�鈭�

2nn2

Short Answer

Expert verified

The limit of the expression 2nn2 is 鈭�

Step by step solution

01

Definition of limits

A limit of a function/expression/sequence is used when the value of the function/sequence cannot be calculated directly or is difficult to calculate at a particular value. It is generally defined as the output obtained when the input is very close to the input value.

01

Given parameters

The given expression is 2nn2and the limit n鈫�鈭�

01

Solve the limits

Take the limit asin the obtained expression and apply the L'H么pital's rule on the expression inside the limit.

Again, apply the L'H么pital's rule in the obtained expression.

As the limit of the exponential function when is , thus the limit of the given expression is 鈭�

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Most popular questions from this chapter

Prove theorem 14.3. Hint: Group the terms in the error as role="math" localid="1657423688910" (an+1+an+2)+(an+3+an+4)+鈰�to show that the error has the same sign as role="math" localid="1657423950271" an+1.Then group them asrole="math" localid="1657423791335" an+1+(an+2+an+3)+(an+4+an+5)+鈰�to show that the error has magnitude less than|an+1|.

Question: Test the following series for convergence

鈭�n=1鈭�(-1)n10nn+2

Show that the binomial coefficients-1n=(-1)n

Estimate the Error if鈭�n=1鈭�xnn3is approximated by the sum of its first three terms for|x|<12.

鈭�0xsintdtt
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