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

Correct option is 1a (100) < 100

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For a positive integer $n,$ let $a (n) = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots + \frac{1}{(2^{n}) - 1} .$ Then

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a (100) < 100

a (100) > 100

a (200) < 100

none of these

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detailed solution

Correct option is A

a(n)=1+12+13+14+⋯+17+18+⋯+115+⋯+12n−1+12n−1+1+⋯+12n−1<1+22+44+88+⋯+2n−12n−1=nThus, a (100) < 100.

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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For a positive integer $n,$ let $a (n) = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots + \frac{1}{(2^{n}) - 1} .$ Then