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

The value of ( _ r=1 ^ [3.2^ -r -2 3^ 1-r ] ) is

Options

  1. A2
  2. B1 2
  3. C1
  4. D0

Correct answer

D. 0

Step-by-step solution

aligned & _ r=1 ^ [3 2^ -r -2 3^ 1-r ] & =3 _ r=1 ^ 1 2^r -2 _ r=1 ^n 3^ 1-r & =3 [ 1 2 + 1 2^2 + ]-2 [1+ 1 3 + 1 3^2 + ] & = 3 2 [1+ 1 2 + 1 2^2 + ]-2 [1+ 1 3 + 1 3^2 + ] & = 3 2 ( 1 1- 1 2 )-2 ( 1 1- 1 3 ) & = 3 2 2- 2 3 2 =0 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