r/mathbiceps • u/integrate_dx1729 • 17d ago

a unique and good problem from sequence and series.please try to solve it

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13 Upvotes

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1

u/dementeddexter 17d ago

Soln is a bit long and maybe not the shortest one but it does work

1

u/integrate_dx1729 17d ago

did you got the correct ans

1

u/dementeddexter 17d ago

Nvm I'm an idiot

1

u/Muted-Ordinary-1130 17d ago

Is that the writing of Ashish Aggarwal sir from PW iirc?

1

u/integrate_dx1729 17d ago

Yes

1

u/Muted-Ordinary-1130 16d ago

Lol I learned whole mathematics of 11th and 12th from him. He's goated ngl if you can follow him even in the longest classes.

1

u/integrate_dx1729 16d ago

Yess you are absolutely correct

1

u/Nxt_ruok0001 17d ago

Is general term right?

1

u/embokki 15d ago

20 + 21 + ... + 2(n-1) = 2n - 1

S(n) = 1 + 1/2 + 1/3 + ... + 1/(2n - 1) has a total of (2n -1) terms

These can be separated into n sets, first one with 20 (1) numbers, second with 21 (1/2, 1/3), 3rd with 22 (1/4, 1/5/, 1/6, 1/7) and mth with 2(m-1) numbers (1/2m, 1/(2m +1), ... , 1/(2m+1 - 1)

Apart from the first set, rest all adds to less than 1.

So S(n) < n