The sum of the series 20C0 - 20C1 + 20C2 - 20C3 + ..... - .... + 20C10 is

Question

The sum of the series 20C0 - 20C1 + 20C2 - 20C3 + ..... - .... + 20C10 is (A) 0 (B) 20C10 (C)  - 20C10 (D)  (1/2) 20C10

Tardigrade Admin · Accepted Answer

(1+x)20=20C0+20C1x+...+20C10x10+...+20C20x20 put x = â 1, 0=20C0-20C1+...-20C9+20C11+...+20C20 0=2(20C0-20C1+...-20C9)=20C10 ⇒ 20C0-20C1+...+20C10=(1/2)20C10.

Q. The sum of the series $^{20} C_{0} -^{20} C_{1} +^{20} C_{2} -^{20} C_{3} + ..... - .... +^{20} C_{10}$ is

0

$^{20} C_{10}$

$^{- 20} C_{10}$

$\frac{1}{2}^{20} C_{10}$

Q. The sum of the series 20C0​−20C1​+20C2​−20C3​+.....−....+20C10​ is

0

20C10​

−20C10​

21​20C10​

(1+x)20=20C0​+20C1​x+...+20C10​x10+...+20C20​x20 put x=−1, 0=20C0​−20C1​+...−20C9​+20C11​+...+20C20​ 0=2(20C0​−20C1​+...−20C9​)=20C10​ ⇒20C0​−20C1​+...+20C10​=21​20C10​.

Q. The sum of the series $^{20} C_{0} -^{20} C_{1} +^{20} C_{2} -^{20} C_{3} + ..... - .... +^{20} C_{10}$ is

$^{20} C_{10}$

$^{- 20} C_{10}$

$\frac{1}{2}^{20} C_{10}$