Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2008MathematicsSequences and Series

_ k=1 ^ 1 k ! ( _ n=1 ^k 2^ n-1 ) is equal to

Options

  1. Ae
  2. Be^2+e
  3. Ce^2
  4. De^2-e

Correct answer

D. e^2-e

Step-by-step solution

aligned & _ k=1 ^ 1 k ! ( _ n=1 ^k 2^ n-1 ) &= _ k=1 ^ 1 k ! [1 (2^k-1 ) ] aligned aligned & = _ k=1 ^ 2^k-1 k ! & = _ k=1 ^ 2^k k ! - _ k=1 ^ 1 k ! & =e^2-1-(e-1) & =e^2-e 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 AP EAMCET PYQs