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Sequences and Series – Sum of Infinite Series

Find the sum of the infinite geometric series:

3 + (3/2) + (3/4) + ….

Integers

( – 25) × ( – 2) =________-

Integers

We get additive inverse of an integer a when we multiply it by _________.

Integers

______________ is the multiplicative identity for integers

Probability – Binomial Distribution

A coin is tossed 5 times. What is the probability of getting exactly 3 heads?

Integers

If we multiply five positive integers and one negative integer, then
the resulting integer is _______.

Integers

If we multiply six negative integers and six positive integers, then
the resulting integer is _______.

Application of Integrals – Area Between Curves

Find the area enclosed between the curves y = x and y = x^2 over the interval [0, 1].

Integers

If we multiply ________ number of negative integers, then the resulting
integer is positive.

Differential Equations – Solution of First-Order DE

Solve the differential equation:

(dy/dx) + y = e^x