Infinite sequences and series
Full explanation, worked examples & memory tricks in the app
Infinite Sequences and Series Prep
English 10 leveled MCQs Free
Shared by a Veda learner · Generated with Veda AI
Smart notes
1
What you'll study, topic by topic
Solved paper preview
Sample questions with model answers
Every question in the paper gets a full exam-length answer in the app — organised by marks, the way a topper writes it.
7 marks Long answer
Derive the Taylor series for $e^x$ around $x = 0$.
Show answer outline
The Taylor series is $e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$.
The full exam-length answer is in the app.
6 marks Long answer
Explain how to determine the convergence of the series $\sum_{n=1}^{\infty} \frac{1}{n^2}$.
Show answer outline
Use the p-series test; since $p = 2 > 1$, the series converges.
The full exam-length answer is in the app.
5 marks Long answer
Calculate the sum of the infinite series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...$.
Show answer outline
The sum is $S = 2$ using the formula for an infinite geometric series.
The full exam-length answer is in the app.
4 marks Medium answer
Describe the ratio test for convergence of series.
Show answer outline
The ratio test states that if $\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| < 1$, the series converges.
The full exam-length answer is in the app.
3 marks Medium answer
Explain the difference between a convergent and a divergent sequence.
Show answer outline
A convergent sequence approaches a limit, while a divergent sequence does not approach any limit.
The full exam-length answer is in the app.
3 marks Medium answer
What is the nth term test for divergence?
Show answer outline
If the limit of the nth term of a series does not equal zero, the series diverges.
The full exam-length answer is in the app.
3 marks Medium answer
What is a power series? Give an example.
Show answer outline
A power series is of the form $\sum_{n=0}^{\infty} a_n (x - c)^n$, e.g., $\sum_{n=0}^{\infty} x^n$.
The full exam-length answer is in the app.
1 marks Short answer
Define convergence of a sequence.
Show answer outline
A sequence converges if it approaches a specific limit as the index goes to infinity.
The full exam-length answer is in the app.
1 marks Short answer
State the formula for the sum of an infinite geometric series.
Show answer outline
The sum is given by $S = \frac{a}{1 - r}$, where $|r| < 1$.
The full exam-length answer is in the app.
1 marks Short answer
What is a divergent series?
Show answer outline
A series is divergent if the sequence of its partial sums does not converge to a finite limit.
The full exam-length answer is in the app.
Study it properly — free, in the app
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.