What is the sum to infinity of the geometric series 8 + 4 + 2 + 1 + ...?
Answer and explanation
Correct answer: D. 16
- Step 1: First term a = 8, common ratio r = 4/8 = 1/2. Step 2. Since |r| < 1, sum to infinity formula applies: S_inf = a / (1 - r). Step 3. S_inf = 8 / (1 - 1/2) = 8 / (1/2) = 16. Answer: 16. Why not the others: 15 is sum of first 4 terms; 32 doubles the sum.
Practise more Algebra, Matrices and Trigonometry.
Free questions with an explanation for every one, and full timed ECAT Pakistan mock tests.
More Algebra, Matrices and Trigonometry questions
- What is the determinant of the 3x3 matrix with rows [1, 2, 3], [0, 4, 5], [0, 0, 6]?
- What is the inverse of the 2x2 matrix A = [[3, 2], [1, 1]]?
- If sin(theta) + cos(theta) = 1, what is the value of sin(2*theta)?
- What is the general solution of the trigonometric equation cos(x) = 1/2?
- How many terms are in the algebraic expansion of (2x + 3y)^10?
- What is the value of the expression: arctan(1/2) + arctan(1/3)?