NDA 2022
Exam NDA
Year 2022
Subject Mathematics
Chapter Sequences and Series NDA 2022 · Mathematics · Sequences and Series
What is the value of aligned & 2(2 × 1)+3(3 × 2 × 1)+4(4 × 3 × 2 ×...
What is the value of
2 ( 2 × 1 ) + 3 ( 3 × 2 × 1 ) + 4 ( 4 × 3 × 2 × 1 ) + 5 ( 5 × 4 × 3 × 2 × 1 ) + … … … … … … + 9 ( 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 ) + 2 ? \begin{aligned} & 2(2 \times 1)+3(3 \times 2 \times 1)+4(4 \times 3 \times 2 \times 1)+ \\ & 5(5 \times 4 \times 3 \times 2 \times 1)+\ldots \ldots \ldots \ldots \ldots \ldots+ \\ & 9(9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)+2 ?\end{aligned} 2 ( 2 × 1 ) + 3 ( 3 × 2 × 1 ) + 4 ( 4 × 3 × 2 × 1 ) + 5 ( 5 × 4 × 3 × 2 × 1 ) + ……………… + 9 ( 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 ) + 2 ? Options A 11 ! B 10 ! C 10 + 10 10+10 10 + 10 D 11 + 10 11+10 11 + 10
Step-by-step solution
2 ( 2 × 1 ) + 3 ( 3 × 2 × 1 ) + 4 ( 4 × 3 × 2 × 1 ) + 5 ( 5 × 4 × 3 × 2 × 1 ) + … … . . + 9 ( 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 ) + 2 = 2 + 2.2 ! + 3.3 ! + 4.4 ! + 5.5 ! + … . + 9.9 ! = 2 ! + ( 2 + 1 ) + 3.3 ! + 4.4 ! + 5.5 ! + … . + 9.9 ! = 3 ! + 3.3 ! + 4.4 ! + 5.5 ! + … . + 9.9 ! \begin{aligned} & 2(2 \times 1)+3(3 \times 2 \times 1)+4(4 \times 3 \times 2 \times 1)+5 \\ & (5 \times 4 \times 3 \times 2 \times 1)+\ldots \ldots..+9(9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times \\ & 2 \times 1)+2 \\ & =2+2.2!+3.3!+4.4!+5.5!+\ldots.+9.9! \\ & =2!+(2+1)+3.3!+4.4!+5.5!+\ldots.+9.9! \\ & =3!+3.3!+4.4!+5.5!+\ldots.+9.9!\end{aligned} 2 ( 2 × 1 ) + 3 ( 3 × 2 × 1 ) + 4 ( 4 × 3 × 2 × 1 ) + 5 ( 5 × 4 × 3 × 2 × 1 ) + …… .. + 9 ( 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 ) + 2 = 2 + 2.2 ! + 3.3 ! + 4.4 ! + 5.5 ! + … . + 9.9 ! = 2 ! + ( 2 + 1 ) + 3.3 ! + 4.4 ! + 5.5 ! + … . + 9.9 ! = 3 ! + 3.3 ! + 4.4 ! + 5.5 ! + … . + 9.9 !
Proceed further we get
= 9 ! + 9.9 ! = 10 ! =9!+9.9!=10! = 9 ! + 9.9 ! = 10 !
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