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7.Binomial Theorem
hard
બહુપદી $(x - 1)(x - 2)(x - 3).............(x - 100)$ ના વિસ્તરણમાં ${x^{99}}$ નો સહગુણક મેળવો.
A
$5050$
B
$-5050$
C
$100$
D
$99$
Solution
(b) $(x – 1)(x – 2)(x – 3)….(x – 100)$
Number of terms $= 100;$
Coefficient of $x^{99} = (x – 1)(x – 2)(x – 3)…(x – 100)$
= $( – 1 – 2 – 3 – …… – 100)$ = $ – (1 + 2 + ….. + 100)$
= $ – \frac{{100 \times 101}}{2} = -5050.$
Standard 11
Mathematics