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1.

The sum to infinity of the geometric series 12 + 6 + 3 + 1.5 + ... equals:

36

Infinity

18

24

2.

The sum to infinity of the geometric series 16 + 8 + 4 + 2 + ... equals:

32

24

64

30

3.

The sum of all coefficients in the expansion of $(3x - 2y)^7$ is equal to:

A) 1

D) 128

C) 0

B) $5^7$

4.

The evaluation of the definite integral $\int_{-\pi/2}^{\pi/2} x^5 \cos x\, dx$ is equal to:

A) $pi^5 / 5$

C) Zero

D) $2pi$

B) 1

5.

What is the rigorous mathematical principle for: Binomial Theorem for Positive Integer Exponent n?

The expansion has exactly n terms

The coefficients nCr always decrease monotonically from start to finish

The expansion of (a + b)ⁿ contains exactly (n + 1) terms, with general term T_(r+1) = nCr * a^{n − r} * b^r

The sum of coefficients in (a + b)ⁿ is equal to n²

Lesson 1 Quiz: Integration Techniques (Substitution and By Parts) and Definite Integrals