24give the soln dear.........ans is rite.[1][1]
let N be positive integer with 1998 decimal digits all of them 1 such that n=1111.......11
Find the thousandth digit after decimall point of √N
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9 Answers
1answer is 1 :)
u'll observe a series
c
11 root .....after deciaml u hav 3166
1111 root ....after decimal u hav 33166
similarly ............for diffrnce of 2
i mean so nw 1998 is d 1998 term
so it will hav 1998/2...... 3's......ie 999 3's
so after 3 u hav 1 .........
so answer is 1
cheero~
1nishu bhayh i wan a golden or else mein mani ka tarika apnaungi ;)
24@ mrunal , i cant get ur method.........
here is my method(a bit bookish) but i cant get anything else..[2][2]
1000th digit after decimal pt. of √N will be unit digit of 101000√N
=>10001000(√101998-1)/3
=>√103998-102000/3
using the fact that,
(101999-7)2<103998-102000<(101999-4)2
=>(101999-7)/3<101000√N<(101999-4)/3
=>33...........31<101000√N<33..........32
=> answer will be 1
any better method is welcome.....i am eagerly waiting for it....
1c
11 root .....after deciaml u hav 3166
1111 root ....after decimal u hav 33166
similarly ............for diffrnce of 2
arey means dekh
jab 2 1's hai so u get 31667 aise kuch after decimal
jab 4 1's hai so u get 33167........
jab 6 1's hai u get 33367
u observe that jitne 1's hai use aadha 3 hai decimal ke baad
so jab 1998 1's hai u hav 999 3's n afetr 3 u hav 1 so 1000th is 1