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1 9 9
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- Apr 2012
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- 0.14
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Thanked: 119-
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- Apr 2012
- 14804
- -
- 0.14
- 598
Thanked: 119
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:
{33} = 33 2194 = 72402
:
[( + 1)( + 2)( + 3) .... (2 )]/[1*2*3* ... *(2 - 1)] = 2^
= 1/2*( + ) =
^2 = *
^2 = *
*/ = * =
( )
> */
48
198
:
= = ( + ) = ( + 2 )
= [3* + 3*]
= [1 ] + [10 ( + )] + [100 ( + 2 )] = [111 * + 210*]
[111 * + 210*] [3* + 3*] = 48
: = 2*
:
= ( + 2 ) = ( + ) = ()
= [1 ( + 2 )] + [10 ( + )] + [100 ] = [ 111* + 12*]
:
[111 * + 210*] - 198 = [ 111* + 12*]
: = 1
:
: 2 3 4
: 432
:
432 - 198 = 234
(432)
11/18
= 18
:
+ + = 11 / 18 .................................................. (1)
1/ + 1/ + 1/ = 18 ................................................ (2)
1/ + 1/ = 2/ .................................................. ...... (3)
(2) (3) > = 1 / 6
(1) (3)
+ = 4 / 9 .................................................. ............. (4)
1/ + 1/ = 12 .................................................. .......... (5)
(4) (5) :
= 1/3
= 1/9
:
+ + = 1/3 + 1/6 + 1/9 = 11 / 18
1/ + 1/ + 1/ = 3 + 6 + 9 = 18
1/ + 1/ = 3 + 9 = 12 = 2*6 = 2*(1/)
1 + 7 + 13 + ................ + = 280
:
= 1
= 6
= 280
=
:
=
= 1 + ( - 1) 6 = 6 - 5
280 = (/2)*[1 + 6 - 5] = (/2)*(6 - 4)
: = 10
= 6 - 5 = 55
:
= 1 = 6 = 10
= (/2)*[2 + ( - 1)*] = (10/2)*[2 + (10 - 1)*6] = 5*56 = 280
: + +
: : : = 1 : 2 : 4
^2 = *
2*( + ) = + ( + ) ... : 2 =
^2 = *(2 ) ............. : = 2
: = 4
: : : = : 2 : 4 = 1 : 2 : 4
:
: ^3 + ^3 = 2
2 = +
* = *
2 ** = * ( + ) = *^2 + *^2
:
: = * = *^2 = *^3
^3 + ^3 = ^3 ^3 + ^3 ^6
= [^2 ^3] + [ ( ^3 )^2] = *^2 + *^2
= 2 **
( / )^ = ^2
= + * + *^2 + ... + *^( - 1) = *(^ - 1)/( - 1)
= ^2 ... ^( - 1) = ^ ^[( - 1)/2]
= 1/ + 1/ + ... + 1/ ^( - 1) = 1/*[1 + 1/ + ... + 1/^( - 1)
= 1/*[(1 - (1/)^)/(1 - 1/)] = [(^ - 1)/(*( - 1)*^( - 1))]
^2 = [^ ^[( - 1)/2]^2 = ^2 ^(*( - 1)]
( / )^ = [[*(^ - 1)/( - 1)] [[(^ - 1)/(*( - 1)*^( - 1))]]^
= ^2 ^(*( - 1))
: ^2 ^2 ^4 - ^2
^2 > 2
^2 ^2 (^4 - ^2)
= 1/2*(^2 + ^4 - ^2) = 1/2*^4
>
( )
:
1/2*^4 > ^2
^2 > 2
3 3 - 2
: ^2 + 9 ^2 > 12
: 3 2
>
3 - > (6**)
^2 + 9 ^2 - 6** > 6**
^2 + 9 ^2 > 12 *
= 30
:
+ + = 30 ............. (1)
2 = + ................ (2)
^2 = ................ (3)
(1) (2)
= 10
= 20 -
(3)
^2 = 10 = 10 (20 - ) = 200 - 10
^2 + 10 - 200 = 0
= 10 > = 10
= - 20 > = 40
:
= 10 = 10 = 10
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- Apr 2012
- 14804
- -
- 0.14
- 598
Thanked: 119:
1 2 3 0000
= =
1 2 3 0000
1 3 5 000
:
1+ 2 + 3 +0000 + = 1/2 ( + 1 )
= 1
= 1
=
= (1 + ( - 1)) =
= 1
= 2
=
= (1 + ( - 1)*2) = 2 - 1
1 = (/2)[2 + ( - 1)]
2 = (/2)[4 + ( - 1)*3]
3 = (/2)[6 + ( - 1)*5]
....
= (/2)[2 + ( - 1)*(2 - 1)]
= (/2)[2 + ( - 1)] = (/2)[ + 1]
= ^2
=
= (/2)[2 + ( - 1)*(2 - 1)] = (/2)[2* - + 1]
1 + 2 + ... + = (/2)[ (/2)[ + 1] + (/2)[2* - + 1]]
= (/2)(/2)[ + 1 + 2* - + 1] = 1/2**[* + 1]
( ) : 0 + 1 +2+.............+ = (+1)^2.
( ) .
( + 1 ) ( ) = ( + 1 )^2
( ) = ^2
= ( + 1 )^2 - ^2 = 2 + 1
0 = (1)^2 = 1
0 + 1 = (2)^2 = 4 > 1 = 4 - 1 = 3
0 + 1 + 2 = (3)^2 = 9 > 2 = 9 - 4 = 5
:
1 - 0 = 2 - 1 = 2
: ( ) = 1 = 2
( )
=
: :
:
( + 1) ( + 2) ( + 3) ( + 4)
^2 + ( + 1)^2 + ( + 2)^2 = ( + 3)^2 + ( + 4)^2
:
= - 2
: - 2 - 1 0 1 2
= 10
: 10 11 12 13 14
: :
:
( - 1) ( - 2) ( - 3) ( - 4)
^2 + ( - 1)^2 + ( - 2)^2 = ( - 3)^2 + ( - 4)^2
= 2
: 2 1 0 - 1 - 2
= - 10
: - 10 - 11 - 12 - 13 - 14
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- Apr 2012
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( 2/ 9 9 2/ 3 3 2 1 0000000)
= 283 /3
:
: 2 /9 2 /3 2 6 18 45 ....
= 2 / 9
= 3
: 9 3 1 1 /3 / 1/9 ...
= 9
= 1 /3
= 2 + 1
:
= + 1
=
283 /3 = [ 2 /9 ( 3^{ + 1} - 1 ) ] / [ 3 - 1 ] + [ 9 ( 1 - (1 /3)^) ] / [ 1 - (1 /3) ]
3^
> 3^ = 243 : = 5
= 2 + 1 = 11
:
= + 1 = 6
= [ 2 /9 ( 3^6 - 1 ) ] / [ 3 - 1 ] = 728 / 9
= = 5
= [ 9 ( 1 - ( 1/3)^5 ) ] / [ 1 - ( 1 /3 ) ] = 121 /9
= 728 /9 + 121 /9 = 849 /9 = 283 /3
( 3 18 1 12 1/ 2 1/ 3 8 1/ 4 0000000 )
= 23.5
: 3 1 1 /3 ....
= 3
= 1 /3
= 3 / (1 - (1 /3)) = 4.5
: 18 12 8 ...
= 18
= 2 /3
= 18 / [ 1 - (2 /3) ] = 54
: /2 /4 ...
=
= 1 /2
= / [ 1 - (1 /2) ] = 2
23.5 = 4.5 + 54 + 2
: = - 17.5
1
2
= =
+ 2 = 2 ( + 5 ) + 1
: = - ( 1 + 8 )
( + 7 )^2 = ( + 3 ) + 2
( 7 + ) = 0 > = - 7 : = 55
:
55 48 41 34 27 20 13 6 - 1 ...
() = 0
+ ( - 1) = 55 + ( - 1) - 7 > = 8 + 6 /8
:
(9) = + 8 = 55 - 8 7 = - 1
(8) = + 7 = 55 - 7 7 = 6
: = 8
(8) = 8 /2 [ 2 + 7 ] = 4 [ 2 55 - 7 7 ] = 244
: 50 - 20
= - 17 : 5
8
:
= =
=
= + 2
= = 50
= ( + 2) = 50 + ( + 1) = - 20 ........ (1)
:
2 = 50 + 3 = 50 + 2
:
() = 50 + ( - 1) ( + 1) = 50 +
[ 50 + + 50 + 2 ] / [ 50 + ( - 1) + 50 + ] = - 17 /5
[ 100 + 3 ] / [ 100 + (2 - 1) ] = - 17 /5 ...... (2)
(1) (2) :
= = 13
= - 5
: 45 40 ...... - 10 - 15
:
50 45 40 35 30 25 20 15 10 5 0 - 5 - 10 - 15 - 20
= + 7 = 50 + 7 - 5 = 50 - 35 = 15
53 47 41 ...
= 53 = - 6
() = + ( - 1)
53 + ( - 1) - 6 = 53 - 6 + 6 = 59 - 6
: 59/6 - < 0 > > 59/6 > = 10
10 = 53 - 9 6 = - 1
9 = 53 - 8 6 = 5
1 2 ..... 9
9
9 = 9/2 [ 2 53 - 8 6 ] = 261
= 4
1/( + 1) 1/( - 2) = 1/4
= 4^2 = 16 > = 16/
1/( + 1) + 1/( - 2) = 2 1/4 = 1/2
^2 - 4 + 4 = 0 > = 2 : = 8
:
2 4 8
1/(2 + 1) = 1/3
1/(8 - 2) = 1/6
1/3 1/4 1/6
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- Apr 2012
- 14804
- -
- 0.14
- 598
Thanked: 119
=
= 27/26
: ^2 ^3 ....
= 2 /(1 - ) > = 1/3
^3 + ^3 ^3 + ^3 ^6 + ^3 ^9 + .... = 27/26
= ^3 = ^3
27/26 = ^3 / ( 1 - ^3 ) = ^3 / ( 1 - {1/3}^3 ) = 27 ^3 / 26
: = 1
: 1 1/3 1/9 1/27 ...
> 0
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- Apr 2012
- 14804
- -
- 0.14
- 598
Thanked: 119
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- Apr 2012
- 14804
- -
- 0.14
- 598
Thanked: 119
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- Apr 2012
- 14804
- -
- 0.14
- 598
Thanked: 119
: 1 (0 1 )
