Question

Ques of Binomial theorem.​

Answer 1

Answer:

1/2(3⁵⁰+1) is sum of coefficient of integral powers of x in the binomial of (1-2√x)⁵⁰

Step-by-step explanation:

Using general expansion

(1-2√x)⁵⁰ = (1+ (-2√x))⁵⁰ = 1 + ⁵⁰c₁(-2√x)¹ + ⁵⁰c₂ (-2√x)² + ⁵⁰c₃ (-2√x)³ --------

We have to find integral power of x so we are intrested in even power of x

∴ Cofficient of integral power = 1+ ⁵⁰c₂2² + ⁵⁰c₄2⁴ + ⁵⁰ c₆ 2⁶ ---------- Desirable value

Expansion of (1+x) ⁵⁰ = 1 + ⁵⁰c₁ x¹ + ⁵⁰c₂x²+⁵⁰c₃x³ ----

let x = + 2 putting in expansion (1+x)⁵⁰

3⁵⁰ = 1+⁵⁰ c₁2¹+ ⁵⁰c₂ 2² + ⁵⁰ c₃ 2³ ------__ (1)

Now, let x= -2 putting in expansion (1+x)⁵⁰

1 = 1 -⁵⁰c₁2¹ + ⁵⁰ c₂ 2² - ⁵⁰ c₃ 3³ ------ __(2)

adding (1)st and (2)nd

then,we get

1+ 3⁵⁰ = 2 + 2 ⁵⁰ c₂2 ² + 2 ⁵⁰ C₄2³ + -----

1+ 3⁵⁰ = 2(1+⁵⁰c₂2² + ⁵⁰ c₄ 2⁴ + ⁵⁰ c₆ 2 ⁶ )

(1+ 3⁵⁰)/2 = 1+⁵⁰ c₂2² + ⁵⁰ c₄ 2⁴ + ⁵⁰ c₆ 2⁶ )

We have get our desirable value

Since, (1+3⁵⁰) /2 is Answer

option (A) is correct

Answer 2

Answer:

option A- is correct.

Step-by-step explanation:

• hope it's helpful.