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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Sequences and Series

NDA 2021 · Mathematics · Sequences and Series

If a_n=n(n!) , then what is a_1+a_2+a_3+ +a_ 10 equal to?

If an=n(n!)a_n=n(n!), then what is a1+a2+a3+…+a10a_1+a_2+a_3+\ldots+a_{10} equal to?

Options

  1. A10!−110!-1
  2. B11!+111!+1
  3. C10!+110!+1
  4. D11!−111!-1

Correct answer

D. 11!−111!-1

Step-by-step solution

∴an=n(n!)=(n+1)n!−n!=(n+1)!−n!\begin{aligned} & \therefore a_n=n(n!)=(n+1) n!-n! \\ & =(n+1)!-n! \end{aligned} Now a1=2a_1=2 ! -1 ! a2=3!−2!a3=4!−3!\begin{aligned} & a_2=3!-2! \\ & a_3=4!-3! \end{aligned}a_{10} \overline{=11!-\ldots 10!}AddingallaboveequationswegetAdding all above equations we geta_1+a_2+a_3 \ldots .+a_{10}=11!-1!$
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