# Precalculus: series solving # Recent questions in Series

Series
ANSWERED ### Missing number in the series 9, ____, 6561, 43046721 is: 81 25 62 31 18

Series
ANSWERED ### Starting with the geometric series $$\sum_{n=0}^\infty x^n$$, find the sum of the series $$\sum_{n=1}^\infty nx^{n-1},\ |x|<1$$

Series
ANSWERED ### Determine whether the geometric series is convergent or divergent. $$10-4+1.6-0.64+...$$ If it convergent, find the sum.

Series
ANSWERED ### Missing number in the series 9, ____, 6561, 43046721 is: 81 25 62 31 18

Series
ANSWERED ### Find the value of x for which the series converges $$\sum_{n=1}^\infty(x+2)^n$$ Find the sum of the series for those values of x.

Series
ANSWERED ### Find the sim of each of the following series. 1) $$\sum_{n=1}^\infty nx^n,\ |x|<1$$ 2) $$\sum_{n=1}^\infty \frac{n}{8^n}$$

Series
ANSWERED ### Let P(k) be a statement that $$\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{k\cdot(k+1)}=$$ for: The basis step to prove $$P(k)$$ is that at $$k = 1, ?$$ is true. for:Show that $$P(1)$$ is true by completing the basis step proof. Left side of $$P(k)$$ and Right side of $$P(k)$$ for: Identify the inductive hypothesis used to prove $$P(k)$$. for: Identify the inductive step used to prove $$P(k+1).$$

Series
ANSWERED ### Determine whether the series is convergent or divergent. $$1+\frac{1}{2\sqrt2}+\frac{1}{3\sqrt3}+\frac{1}{4\sqrt4}+\frac{1}{5\sqrt5}+\dots$$

Series
ANSWERED ### Use the formula for the sum of a geometric series to find the sum, or state that the series diverges. $$\displaystyle{\frac{{{25}}}{{{9}}}}+{\frac{{{5}}}{{{3}}}}+{1}+{\frac{{{3}}}{{{5}}}}+{\frac{{{9}}}{{{25}}}}+{\frac{{{27}}}{{{125}}}}+\ldots$$

Series
ANSWERED ### Write the series and find the sum of the series of sigma notation. $$\displaystyle{\sum_{{{i}={0}}}^{{6}}}{\frac{{{i}}}{{{i}-{1}}}}$$

Series
ANSWERED ### Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. $$\displaystyle{\sum_{{{n}={1}}}^{\infty}}{\frac{{{1}}}{{{n}+{3}}}}$$

Series
ANSWERED ### Write out the first eight terms of each series to show how the series starts. Then find the sum of the series or show that it diverges. $$\sum_{n=2}^\infty\frac{1}{4^n}$$

Series
ANSWERED ### Solved examples of number series in Quantitative aptitude As we know, questions related to number series are very important in Quantitative aptitude section, So, today I’m going to discuss some problems of number series. These are just for your practice. I have already discussed this chapter in previous session i.e. Sequence and Series. Read this article first, then go through these examples.

Series
ANSWERED ### Find the power series representation for g centered at 0 by differentiating or integrating the power series for f(perhaps more than once). Give the interval of convergence for the resulting series. $$g(x)=\ln(1-2x)$$ using $$f(x)=\frac11-2x$$

Series
ANSWERED ### Working with binomial series Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Maclaurin series for the following functions. Use the Maclaurin series $$(1+x)^{-2}=1-2x+3x^2-4x^3+\cdots\ for\ -1$$ $$(1+4x)^{-2}$$

Series
ANSWERED ### In series A, the first term is 2, and the common ratio is 0.5. In series B, the first term is 3, and the two infinite series have the same sum. What is the ratio in series B?​

Series
ANSWERED ### Q1. Does a series $$\displaystyle{\sum_{\infty}^{{{n}={1}}}}{b}{n}$$ converge if $$bn \rightarrow 0$$? Justify your answer by at least two examples?

Series
ANSWERED ### Find a formula for the nth partial sum of each series and use it to find the series’ sum if the series converges. $$\frac{9}{100}+\frac{9}{100^2}+\frac{9}{100^3}+...+\frac{9}{100^n}+...$$

Series
ANSWERED ### Write the following arithmetic series in summation notation. $$8+10+12+\cdots+34$$
ANSWERED 