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Question

For a positive integer n,let a(n)=1+12+13+14+...+1n Then

A
a(100)<100
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B
a(100)>100
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C
a(200)<100
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D
a(200)>100
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Solution

The correct options are
A a(100)<100
C a(200)<100
a(n)=1+12+13+14++1n , where nZ+
Let us consider a series b(n)
b(n)=1+12+12+12++nterms
Using comparison test, b(n)>a(n) always
Putting n=200,b(200)>a(200)
1+1992>a(200)a(200)<100.5100
Now, let c(n)=1+1+1++nterms
c(n)>a(n)
Putting n=100,c(100)>a(100)
a(100)<100
Hence, all options are incorrect

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