The value of Σ (-1)^{k+1} [k(k+1)/k!] is

The value of Σ (-1)^{k+1} [k(k+1)/k!] is

Q. The value of Σ (-1)^k+1 [k(k+1)/k!] is

(A) e/2

(B) √e

(C) 2/e

(D) 1/e

Correct Answer: 1/e

Explanation

Consider the given series:

Σ (-1)^k+1 k(k+1)/k!

Rewrite the numerator:

k(k+1) = k² + k

So the series becomes:

Σ (-1)^k+1 (k²/k! + k/k!)

Using standard results:

Σ (-1)^k / k! = 1/e

Σ (-1)^k k / k! = -1/e

Σ (-1)^k k² / k! = 1/e

Substitute and simplify:

Required sum = 1/e

Hence, the value of the given series is 1/e.

Related JEE Main Questions

Let z be a complex number such that |z − 6| = 5 and |z + 2 − 6i| = 5. Then the value of z³ + 3z² − 15z + 141 is equal to

If tan(A − B)/tan A + sin²C/sin²A = 1, A, B, C ∈ (0, π/2), then

If g(x) = 3x² + 2x − 3, f(0) = −3 and 4g(f(x)) = 3x² − 32x + 72, then f(g(2)) is equal to:

The area of the region R = {(x, y) : xy ≤ 8, 1 ≤ y ≤ x², x ≥ 0} is

Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,

JEE Main Chapter-wise Previous Year Questions