^ 16 _ r+2 ^ 16 C_r= - Vidyadip

MCQ

$\sum\limits^{16}_{\text{r}+2}{^{16}}\text{C}_\text{r}=$

A
2¹⁵ - 15
B
2¹⁶ - 16
C
2¹⁶ - 17
D
2¹⁷ - 17

✓

Answer

2¹⁶ - 17

Solution:

Consider given the binomial expression,

$\sum\limits^{16}_{\text{r}+2}{^{16}}\text{C}_\text{r}={^{16}}\text{C}_{2}+{^{16}}\text{C}_{3}+{^{16}}\text{C}_{3}+\ .....\ {^{16}}\text{C}_{16}$

$=2^{16}-17$

Hence, this is the answer.

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