math-algebra short techniques and formulas by tanbircox

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Want more Updates http://facebook.com/tanbir.ebooks facebook /gmail/skype: - http://tanbircox.blogspot.com আনায ফু ক ফা pdf রযডারযয Menu Bar এয View অনরি তে রিক করয Auto /Automatically Scroll অনরি কন (অথফা যারয তমরে Ctrl + Shift + H )এফায up Arrow ফা down Arrow তে রিক করয আনায ড়ায ু রফধা অনুারয র ীড রিক করয রনন। ( )( ) ( ) ( ) −−−−−(x) ( ) . / . / ( − ) −−−−−(y) ( − ) . / . − / ( ) ( − ) ( ) [ (x) +(y)] () () ( ) − ( − ) [ (x) − (y)] ⇛( ) ( − ) ⇛( − ) ( ) () ()

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    pdf Menu Bar View Auto /Automatically Scroll

    ( Ctrl + Shift + H ) up Arrow down Arrow

    ( )( ) ( )

    ( ) (x)

    ( )

    .

    / .

    /

    ( ) (y)

    ( )

    .

    / .

    /

    ( ) ( ) ( ) [ (x) +(y)]

    ( ) ( )

    ( ) ( ) [ (x) (y)]

    ( ) ( )

    ( ) ( ) ( ) ( )

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    ( )

    ( ) ( )

    ( ) ( ) ( ) ( )

    ( )( )( ) ( ) ( )

    ( )

    ( ) ( )

    ( )

    ( ) ( )

    ( )( )

    ( ) *( ) ( ) ( ) +

    ( ) ( ) ( ) ( )( )( )

    ( )( )

    ( )( )

    ( )( )

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    , q (a b ) x q (q= a+b) r (r=ab) ( ) ( )( )

    1) q>0, r>0 ( )( )

    2) q0 ( )( )

    3) q>0, r

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    a (n a )

    ( )

    ( )

    ( ) ( )

    . /

    ( )

    x =y

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    a n

    10

    x =

    x =

    ( )

    .

    /

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    , MCQ , MCQ Answer Choice x y x y ( )

    ,

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    1(First Term) n(Last Term) (Common Difference) =Second term first Term = 1

    (Number of Terms) =

    + 1

    (Sum of the Series) =

    =

    ( )

    (Avarage of the Series) =

    =

    a + (a+d) + (a+2d) ( d) n ,

    = a

    d =

    = n

    n ( ) (n )d

    n =

    n =

    * (n )d+

    , = a

    r =

    = n n =

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    r >0 1 r ,

    n

    r < 0 1 r (.1 -.9 ) ,

    n

    -1

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    1, 4, 9, 16. 5, 5 ]

    1 , 9 , 25, 49, 81 , 5 7 9 ]

    9 36 81 144 .. 5, ( ) ( ) ]

    81, 27, . 3, 1 9 , ]

    1, 2, 3, 5, 8 , 13 , 21 , 34. 55[ = ]

    8, 11, 17, 29, 53,.. 101 [8, 8+(11-8),11+(17-11), ]

    1, 3, 6, 10, 15, 21,. 28 [ 1,(1+2),(3+3),(6+4), (10+5)]

    2, 8, 18, 32, 50 [ 2,(2+6),(8+6+4),(18+6+4+4), (32+6+4+4+4)]

    2, 4, 8, 14, 22, 32. 44 [ 2,(2+2),(4+2+2),(8+2+2+2), (14+2+2+2+2)]

    0, 5, 12, 21, 32.. 45 [ 0,(0+5),(5+5+2),(12+5+2+2), (21+5+2+2+2)]

    13, 17, 25, 41,.. 73 [ 13,(13+22),(17+23),(25+24), (41+25)]

    5, 7, 11, 19,.. 5 [ 5,(5+21)(7+22),(11+23),(19+24)]

    8 [ 4,(4+21)(6+22),(10+23),(18+24)]

    3, 6, 4, 9, 5, 12, 6,. 5 , t1:t3:t5:t7 5 | t2:t4:t6:t8 9 5-

    8 9 7 , (t1 +4),(t2+8)(t3+4)(t4+8)]

    7 5 5 8 9

    , t3:t5:t7 ( 7-2),(27-4),(27-6),(27-8)| t4:t6:t8 (5 ) (5 ) (5 9)-

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    0, 9, 17, 2435, 39, 42 .

    5 8

    1, 3, 6 9 5 8

    7

    7 5

    7 9 5

    9

    7 8 5 5 9 7

    7 5 9 7 5

    15, 13, 12, 11, 9, 9..

    7 8 8 7

    8 5 8 9

    9 7 5 8

    9 5 7 99

    5 7

    5 7 7

    5 8 7 8

    9 7 5 5 8

    21, 18, 9 7

    8 5 5 9

    5 9

    7 7 5 5

    5 9 5 5

    5 7

    7 8 8 8 8

    3, 7, 28, 32, 8, 12, 48, 5

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