The sum of the series 20 c 0-20 c 1-20 c 2-20 c 3- 20 C 10 isA- -20 C 10B- 0C- 20 C 10D- 1-220 C 10

The correct option is D S = 20C_0 20C_1 + 20C_2 + .......+20C_10 nbsp; S = 20C_20 20C_19 + ........... + 20C_11 + 20C_10 nbsp; 2S = 20C_0 20C_1 + .. ...

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Byju's Answer

Standard XII

Mathematics

Sigma n

The sum of th...

Question

The sum of the series $20_{c_{0}} - 20_{c_{1}} + 20_{c_{2}} - 20_{c_{3}} + . . . 20_{c_{10}} i s$

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Solution

The correct option is B

S = $20 C_{0} - 20 C_{1} + 20 C_{2} + . . . . . . . + 20 C_{10}$

$S = 20 C_{20} - 20 C_{19} + . . . . . . . . . . . + 20 C_{11} + 20 C_{10}$

$2 S = 20 C_{0} - 20 C_{1} + . . . . . . . . . . . . + 20 C_{9} + 20 C_{10} + 20 C_{10} + 20 C_{10} - 20 C_{11} + . . . . + 20 C_{20}$

= $20 C_{10} \Rightarrow S = \frac{1}{2} (20 C_{10})$

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The sum of the series 20c0−20c1+20c2−20c3+...20c10 is

The correct option is B S = 20C0−20C1+20C2+.......+20C10 S=20C20−20C19+...........+20C11+20C10 2S=20C0−20C1+............+20C9+20C10+20C10+20C10−20C11+....+20C20 = 20C10⇒S=12(20C10)

The sum of the series $20_{c_{0}} - 20_{c_{1}} + 20_{c_{2}} - 20_{c_{3}} + . . . 20_{c_{10}} i s$