Question

Value of (1÷1*2+1÷2*2+1÷3*2)

Answer 1

$\huge{ \mathbb \red{QUESTION:-}}$

VaLuE oF (1÷1*2+1÷2*2+1÷3*2)

$\huge \sf 3.66666666667 \: {\mathcal \purple{AnSwEr}}$

Answer 2

Answer:

1/(2²) is 1/1² - 1/2²

Which is (2²-1²)/2², which simplifies to,

(3)(1)/(2²)

Next term gives, (4)(2)/(3²)

The next is (3)(5)/4²

So, final product = 1×2×3²×4²….2016²×2017×2018/[2²×3²….2017²]

Multiplying numerator and denominator by 2,

We get, (2016!)² × (2017×2018)/2×(2017!)²

= 2018/2×2017

= 1009/2017 = 0.50024…..

Thank you!

=>.[{1}^2-{1/2}^2]×[{1}^2-{1/3}^2]×[{1}^2-{1/4}^2]…………[{1}^2-{1/2016}^2]×[{1}^2-{1/2017}^2

=>(1–1/2)(1+1/2)×(1–1/3)(1+1/3)×(1–1/4)(1+1/4)×……..×(1–1/2016)(1+1/2016)×(1–1/2017)(1+1/2017).

=> 1/2×3/2×2/3×4/3×3/4×5/4××××××××××××2015/2016×2017/2016×2016/2017×2018/2017

=> 1/2×2018/2017 [All the fractions cancell each -other except first and last fraction.]64

=> 1009/2017. Answer.

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It is a very simple solution.

You just need to write the first step, go on a push and the answer emerges.

I have attached an image. The solution procedure is also available on my youtube video channel.

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How do I evaluate (1−122)(1−132)...(1−120062)(1−120072) ?