Maths doubt

Can someone explain me how the formula comes for question 10 (theory) (determinants wala) no need to solve it

Plz solve question 9

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when you get the drs for 3 of each plane and put it in the form of [a b c] axb reprsents area vector of base (comparing to standard cuboid) and c costheta (theta is the angle between axb and c) is the component of height along z axis . so if you mulitply all you get (axb)c costheta or [a b c]

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Adding Diagrams to your explanation :sweat_smile:


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9 th vala mera lagbhag sab ho gya h par aakhri me dikkat ho rhi hai @VictoryGod mai apna solution bhej rahaek sec

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For q10 see this

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Bro I got the next step

Here u have to use this inequality

2(√(n+1) - √n) < 1/√n < 2(√n-√(n-1))

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thanks bhai

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Sorry to disturb you people for stupid things but how is this inequality derived?

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Using sandwich theorem I think

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It is written something like this
Average of root value of n+1,n

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I know this is not proof but i observed it for summation

Uh…sorry but I don’t understand the logic here :disappointed_relieved:

You can replace the summation with an integral. (This usually gives an accurate result. Here we have integral 1/sqrt(x) from 1 to 100). If I remember correctly, the maximum possible error between the integral and summation is (minimum term of the sequence)/2

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\sqrt{n+1} - \sqrt{n} = \frac{1}{\sqrt{n+1} + \sqrt{n}} < \frac{1}{\sqrt{n} + \sqrt{n}} = \frac{1}{2\sqrt{n}}<\frac{1}{\sqrt{n}+\sqrt{n-1}} = \sqrt{n}-\sqrt{n-1}

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Showdown begins yay
Everyone posting solutions take look into my veryy unique yet basic proof @Uzumaki_129 @Anvita @complexroots

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:sunglasses::sunglasses::sunglasses:

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Nice

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Bg music: Snoop Dogg XD

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Thank you @complexroots @Uzumaki_129 @VictoryGod

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