(MTH 101) Elementary Mathematics 1 Mock Exam 1

For a geometric series $\sum ar^n$ to converge to a finite sum to infinity, which condition must the common ratio $r$ satisfy?

By the principle of mathematical induction, for every positive integer $n$, the expression $4^n + 15n - 1$ is divisible by which number?

For every positive integer $n$, the expression $n^3 + 2n$ is always divisible by which number?

Find the linear approximation of $\sqrt[3]{7.992}$.

If $Z = 1+i$, find $Z^2$.

Find the numerical coefficient of the 4th term in the binomial expansion of $(x - 2y)^{10}$.

In an Arithmetic Progression, the sum of the first $n$ terms is given by $S_n = 2n^2 + 3n$. Find the $n^{th}$ term ($a_n$).

If $Z_1 = 1+i$ and $Z_2 = 3-i$, find the modulus of $Z_1 Z_2$.

In the principle of mathematical induction, the propositional statement $P(n)$ is true for which set of numbers?

Find the term independent of $x$ in the expansion of $(2x - 1/x)^4$.