hints

[sage jackal]

How to do this?

[covert steeple]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[dense bay]

a<b<c trivially

just compare c and d

[sage jackal]

All terms are positive

In C so i feel C is biggest but answer key says D

[dense bay]

so what

$C=\sum_{k=0}^{32}\binom{32}{k}^2=\binom{64}{32}$

[frosty kestrel]

#EqualityForWolf

[sage jackal]

Wolf bhai???

Owwww nice nice

62,32 kaise aaya?

[dense bay]

$\sum_{k=0}^{n}\binom{n}{k}^2=\binom{2n}{n}$

[sage jackal]

Formula h kya nc0ncn??

[frosty kestrel]

#EqualityForWolf

[dense bay]

generating function se prove hojayega

coefficient of (x^n) in expansion of ((x+1)^n(1+x)^n)

[frosty kestrel]

#EqualityForWolf

[dense bay]

and D option

generating function se prove hojayega

[sage jackal]

Hmm all pairs

0 n
1 n-1
...

n 0

a0^2+a1^2...man^2

[dense bay]

coefficient of (x^n) in ((1+x)^n(1-x)^n=(1-x^2)^n)

[sage jackal]

Yooo

Nice nice

Minus

Ohh let me change in sign again

[frosty kestrel]

#EqualityForWolf

[sage jackal]

(1+x)^n (x-1)^n?

No?

[dense bay]

n even

[dense bay]

nah

i mean

haan

series ke liye

kar sakta hai

actually

[sage jackal]

1-x^2)^n = 1-x^2+x^4-x^6...

[dense bay]

No?

if $n$ is odd the coefficient of $x^n$ is $0$ but if it is even then the coefficient of $x^n$ is $(-1)^{\frac{n}{2}}\binom{n}{n/2}$

[frosty kestrel]

#EqualityForWolf

[sage jackal]

Lekin bhai (1-x^2)^n me cofficent C^2 kaise hoga?

[dense bay]

((1-x)^n (1+x)^n)

[frosty kestrel]

#EqualityForWolf

[dense bay]

,

[sage jackal]

@dense bay

[hazy acorn]

this is not readable

[sage jackal]

D is big

@dense bay @hazy acorn

[hazy acorn]

we will not check your calculations

although we can confirm if your ideas are correct

so tell us the idea instead

[sage jackal]

Okay baby

Sweetboy