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MathsJEE Main 28 Jan 2026, Shift 1·Q2·MCQ·Moderate

Sequences & Series · Exponential series sum

The value of ∑k=1∞(−1)k+1(k(k+1)k!)\displaystyle\sum_{k=1}^{\infty}(-1)^{k+1}\left(\frac{k(k+1)}{k!}\right) is:
  1. (1)2/e2/e
  2. (2)1/e1/e
  3. (3)e\sqrt{e}
  4. (4)e/2e/2

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See the full 28 Jan 2026, Shift 1 paper