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SIA PUBLICATION-FUNCTIONS AND MATHEMATICAL INDUCTION -Problems
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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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- The function f : C to C defined by f(x)=(ax+b)/(cx+d) for x in C, whe...
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- If N denotes the set of all positive integers and if f : N to N is def...
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- {n(n+1)(2n+1):n in 1} sub
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- If f : N to Z is defined by f(x)={{:("2 if "n = 3k" , " k ...
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- The function f:R rarrR is defined by f(x)=3^(-x). Observe the followin...
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- If n in N , and the period of (cos nx)/(sin(x//n)) is 4pi , then n=
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- If f(x)={{:([x]","if-3lt x le-1),(|x|","if-1 lt x lt 1),(|[x]|","if 1 ...
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- sum(k=1)^(5)(1^(3)+2^(3)+…+k^(3))/(1+3+5+….+(2k-1)) is equal to
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