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STATISTICS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSTATISTICS1 Mark
MCQ
The sum $ \displaystyle \sum _{\text{ r}=1 }^{ 10 }{ \left( {\text{ r} }^{ 2 }+1 \right) \times \left( \text{r}\ ! \right) }$ is equal to:
  • A
    (11)!
  • ✓
    10 × (11)!
  • C
    101 × (10)!
  • D
    11 × (11)!
✓

Answer

Correct option: B.
10 × (11)!
$ \sum(\text{r}^2+1)\text{r}!=\sum[\text{r}(\text{r }+1) -(\text{r}-1)\text{r}!$
$ =\sum\limits^{10}_\text{r=1}[\text{r}(\text{r }+1)!-(\text{r}-1)\text{r}!]$
$= (1×2!−0×1!)+(2×3!−1×2!)+......+(10×11!−9×10!)=10×11!​ $

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