(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] prove the formula of squareroot 2

Verify the following formula:

Squareroot (2)=7/5*(1+ 1/100 + 1*3/(100*200) + 1*3*5/(100*200*300) + etc..)

Use the Fact that 50=5^2*2=7^2+1

Theorem: (1+x)^a=1 +a*x/1 + (a(a-1)*x^2)/(1*2)+ (a(a-1)(a-2)*x^3)/(1*2*3)+ etc...

Hint: use the theorem with (1-x)^(-1/2)

I used the series expansion for (1-x)^(-1/2) and got

(1-x)^(-1/2)=1+ (1*x)/(1*2)+(1*3*X^2)/(1*2*4)+ (1*3*5*x^3)/(1*2*4*6)+etc ....

I do understand that the squareroot (50)=5*squareroot(2) But I am stuck

Please help, thanks

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# Homework Help: Prove the formula of squareroot 2

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