What is the sum of the term in the infinite series \(1+\dfrac{1}{2}+\dfrac{1}{4}+...\)?

What is the sum of the first 51 consecutive odd positive integers?

What is the sum of the terms in the geometric series 1 + 4 + 16 + ... + 1024?

Three consecutive terms in an arithmetic sequence are x, 2x + 11 and 4x − 3. What is the constant difference between consecutive terms in this sequence?

What is the sum of the terms in the arithmetic series 2 + 5 + 8 + 11 + 14 + ... + 89 + 92? 

The first three terms of a sequence are 1, 2 and 3. Each subsequent term is the sum of the three previous terms. What is the 11th term of this sequence?

The first four stages of a dot pattern are shown. How many more dots are in the figure at Stage 47 than in the figure at Stage 27?

A five-digit number is made by randomly ordering the digits 1, 2, 3, 4 and 5. What is the probability that this number is divisible by 4? Express your answer as a common fraction.

What is the percent probability that a randomly selected multiple of 3 less than or equal to 3000 is also a multiple of 5?  

When the circuit containing blinking lights A and B is turned on, lights A and B blink together. Then A blinks once every 5 seconds and B blinks once every 11 seconds. Lindsey looks at the two lights just in time to see A blink alone. What is the percent probability that the next light to blink will be A blinking alone?  

A penny, a nickel and a dime are flipped. What is the probability that at least two coins land heads up and one of them is the nickel? Express your answer as a common fraction.

A drawer contains five socks: two green and three blue. What is the probability that two socks pulled out of the drawer at random will match? Express your answer as a common fraction. 

A bag contains five chips numbered 2 through 6. Danya draws chips from the bag one at a time and sets them aside. After each draw, she totals the numbers on all the chips she has already drawn. What is the probability that at any point in this process her total will equal 10? Express your answer as a decimal to the nearest tenth.

Max has eight identical cups. Each cup contains a different combination of nickels, dimes and quarters, each totaling 45 cents. Max randomly selects a cup. What is the probability that the cup he selects contains at least three dimes? Express your answer as a common fraction.

Petra randomly selects a card from a standard deck of 52 playing cards. What is the percent probability that the card shows a red number greater than 6? Express your answer to the nearest hundredth.

How many equilateral triangles can be formed within the same plane using at least two vertices that are also vertices of a given regular hexagon?

A three-digit number is created with three different digits from the set {1, 2, 3, 4, 5}. What is the probability that the number is a multiple of 15? Express your answer as a common fraction.

How many people would have to be in a room such that it is certain  of them have the same birth date?

Find the last three-digit numbers of: \(M=2^{2018}\) 

Find the last three digit-numbers of: \(E=2^{2017}\)