JEE Mains · Maths · STD 11 - 8. sequence and series
The value of \(\left(2 .{ }^{1} P _{0}-3 .{ }^{2} P _{1}+4 .{ }^{3} P _{2}-\ldots .\right.\) up to \(51\) th term)+\(\left(1 !-2 !+3 !-\ldots . .\right.\) up to \(51^{\text {th }}\) term \()\) is equal to
- A \(1+(51) !\)
- B \(1-51(51) !\)
- C \(1+(52) !\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(1+(52) !\)
Step-by-step Solution
Detailed explanation
\(S =\left(2 \cdot{ }^{1} P _{0}-3 .{ }^{2} p _{1}+4 .{ }^{3} p _{2} \ldots \ldots \ldots\right.\) upto 51 terms \()\) \(+(1 !+2 !+3 ! \ldots \ldots \ldots .\) upto 51 terms \()\) \(\left[\because{ }^{n} p_{n-1}=n !\right]\) \( \therefore \quad S =\)…
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