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SIA PUBLICATION-FUNCTIONS AND MATHEMATICAL INDUCTION -Problems
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- If a,b and n are natural numbers, then a^(2n-1)+b^(2a-1) is divisible ...
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- Let R denote the set of all real numbers and R^(+) denote the set of a...
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- The numbers a(n)=6^(n)-5n for n=1,2,3,… whrn divided by 25 leave the r...
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- If f:[2, 3] rarr RR is defined by f(x)=x^(3)+3x-2, then the range f(x)...
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- {x in RR:(2x-1)/(x^(3)+4x^(2)+3x) in RR}=
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- Using mathematical induction, the numbers a(n)'s are defined by, a...
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- If RR rarrC is defined by f(x)=e^(2ix)" for x in RR then, f is (where ...
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- If f:[-6, 6]rarr RR defined by f(x)=x^(2)-3" for " x in R then (fofof...
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- If f:Rrrarr RR and g: RR rarr RR are defined by f(x)=|x| and g(x)=[x-3...
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- For any integer n ge 1 , the sum sum(k=1)^(n)k(k+2) is equal to
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- If f:R rarr R is defined by f(x)=(1)/(2-cos 3x) for each x in R then t...
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- If f : R to R and g : R to R are defined by f(x)=x-{x} and g(x)=[x] fo...
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- If S(n)=1^(3)+2^(3)+…+n^(3) and T(n)=1+2+….+n, then
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- If f:RR rarr RR is defined by f(x)=x-[x] -(1)/(2)" for "x in RR, where...
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- If f:R rarr R is defined by f(x)=[2x]-2[x] for x in R, then the range ...
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- If f : R to R is defined by f(x) = {{:(x+4" for " x lt - 4),(3x+2" ...
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- For all integers, n ge 1 which of the following is divisible by 9.
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- {x in R : [x-|x|=5} is equal to
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