Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2018MathematicsSequences and Series

The sum to n terms of the series 1 2 + 3 4 + 7 8 + 15 16 + is

Options

  1. A2^n-1
  2. B1-2^n
  3. Cn+2^n-1
  4. Dn-1+2^ -n

Correct answer

D. n-1+2^ -n

Step-by-step solution

aligned & 1 2 + 3 4 + 7 8 + 15 16 + upto n terms & = (1- 1 2 )+ (1- 1 4 )+ (1- 1 8 ) upto n terms & =(1+1+1+ n terms ) & - ( 1 2 + 1 2^2 + 1 2^3 + n terms ) & =n- 1 2 (1- 1 2^n ) 1- 1 2 =n-1+ 1 2^n =n-1+2^ -n aligned

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Every term of a geometric progression is positive , and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is: 2026If k is the arithmetic mean of two given quantities and p, q are the geometric means between the same two quantities, then p^3 + q^3 is: 2026Let ' a ' and ' b ' be two numbers where a < b . The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 2 2026The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14. Find the numbers. 2026Let a₁, a₂, a₃, be a geometric progression of positive integers such that a₁ = 3 and a_ n+2 - 2a_n = a_ n+1 for all positive integers n . What is the value of a₁ + a₂ + a₃ + a₄ + a 2026The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is 2026If we insert two numbers between 2 and 4 so that the resulting sequence is in G.P, then the inserted numbers in the order are 2026If S _ n =1^3+2^3+ . .+ n ^3 and T _ n =1+2+ . .+ n , then 2025 Full Sequences and Series list All Manipal MET PYQs