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Prove that for n=1, 2, 3... [(n+1)/2]+[...

Prove that for `n=1, 2, 3...` `[(n+1)/2]+[(n+2)/4]+[(n+4)/8]+[(n+8)/16]+...=n` where `[x]` represents Greatest Integer Function

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ARIHANT MATHS-FUNCTIONS-Exercise For Session 4
  1. f(x)=sqrt(x^(2)-abs(x)-2) . Find the domain of f(x).

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  2. f(x)=sqrt(2-abs(x))+sqrt(1+abs(x)). Find the domain of f(x).

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  3. f(x)=log(e)abs(log(e)x). Find the domain of f(x).

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  4. f(x)=sin^(-1)((2-3[x])/4), which [*] denotes the greatest integer func...

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  5. f(x)=log(x-[x]), where [*] denotes the greatest integer function. find...

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  6. f(x)=1/sqrt([x]^(2)-[x]-6), where [*] denotes the greatest integer fun...

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  7. f(x)= cosec^(-1)[1+sin^(2)x], where [*] denotes the greatest integer f...

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  8. f(x)=cos^(-1)sqrt(log([x])""abs(x)/x), where [*] denotes the greatest ...

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  9. f(x)=sqrt((x-1)/(x-2{x})), where {*} denotes the fractional part.

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  10. Domain of f(x)=sin^(-1)(([x])/({x})), where [*] and {*} denote greates...

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  11. f(x)=sin^(-1)[2x^(2)-3], where [*] denotes the greatest integer funct...

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  12. Find the domain and range of the following function: f(x)=sin^(-)[lo...

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  13. The domain of f(x)=sqrt(2{x}^2-3{x}+1), where {.} denotes the fraction...

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  14. f(x)=1/((x-2)+(x-10)-8)Find integration of f(x)

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  15. If a function is defined as f(x)=sqrt(log(h(x))g(x)), where g(x)=|sinx...

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  16. The number of solutions of the equation [y+[y]]=2cosx, where y=(1)/(3)...

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  17. Prove that for n=1, 2, 3... [(n+1)/2]+[(n+2)/4]+[(n+4)/8]+[(n+8)/16]+...

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  18. Find the integral solutions to the equation [x][y]=x+y . Show that all...

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