Algebra

If $P(n)$ is $2n + 1 < 2^n$, what is the smallest natural number $n$ for which the base case $P(n)$ is true?

If $P(n)$ is $1 + \frac{1}{4} + \frac{1}{9} + \dots + \frac{1}{n^2} < 2 - \frac{1}{n}$, then $P(2)$ is:

The statement $P(k) \implies P(k+1)$ is called the:

If $x + iy = i$, find the value of the real part $x$.

For the general quadratic equation $ax^2 + bx + c = 0$, what is the formula for the sum of the roots?

If one root of the quadratic equation $x^2 + 9 = 0$ is $3i$, what is the other root?

If $x \in \{0, 1, 2, 3, 4, 5\}$, what is the solution for $2x - 3 > 4$?

What is the solution of $\frac{x}{3} + 4 > 4$ for $x \in R$?

Solve $1 - x < 2$.

Solve for $n$ if $\frac{n!}{(n-2)!} = 6$.

How many 5-digit numbers can be formed using the digits $\{1, 2, 3, 4, 5\}$ such that each digit is used exactly once?

Calculate the value of $^5C_2$.

What is the second term in the expansion of $(x + 2)^4$?

The coefficient of $x^2$ in the expansion of $(1 - x)^3$ is:

The value of $^nC_r / ^nC_{n-r}$ is:

What is the common ratio of the GP sequence: $\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \dots$?

Find the $7^{th}$ term of the AP: $7, 14, 21, \dots$.

Find the $4^{th}$ term of a GP where $a = 1$ and $r = 10$.