jewel’s carejewelscare.weebly.com/uploads/1/1/0/7/110728531/ssc_sosimdhara_2017_page.pdfjewel’s...

Jewel’s Care Life is for motto lesson


www.jewelscare.weebly.com Youtube Chennal Name : Jewel’s Care

Jewel’s Care Life is for motto lesson…..

S.S.C. Math

Chapter : Finite Series ( ) By optimum usage of time and minimum wastage of time, you can buildup yourself. So, don’t worry about your career.

It’s yours MD Ibrahim Khalil Jewel

2017

Prepared & Organized by : MD Ibrahim Khalil Jewel

( Math teacher of Orbit Coaching Center/Admission care)

MO: 01677836677

Gmail : [email protected]

Demra, Dhaka - 1362

mailto:[email protected]




Series

( Sequence ) : N = {1,2,3,4,5,………}

( Series ) : 1+3+5+7+……… / 2+4+8+………

SSC

→ 2+4+6+8+10+12+14+16+18=90

, , a = 2 [ the first letter of alphabet ]

, d → 4-2=2 [ d = the common difference of all terms ]

→ 6-4=2 [ ]

→ 8-6=2

/ n / p = 18

, n = 9

n / 9 / , Sn = 90

≠

→ n , p = a+(n-1)d [ , a d ]

→ n , Sn =

{2a+(n-1)d} Sn =

(a+p)

→ 1+1+1+1+1+1+1+…… = n.1

→ d+d+d+d+d+d+d+….… = n.d

→ (a+p)+(a+p)+(a+p)+…… = n.(a+p)




→ 2+4+8+16+32=62

, , a = 2 [ the first letter of alphabet ]

, q/r →

= 2 [ r = the common ratio of all terms ]

→

= 2 [ ]

→

= 2

/ n / p = 32

, n = 5

n / 9 / , Sn = 62

, n ≠ n [ ]

→ n = arn-1

[ , a r ]

→ n , Sn =

[ , r > 1 ]

→ n , Sn =

[ , r ˂ 1 ]

→ n / 1+2+3+4+……+n =

→ n / 13+2

3+3

3+4

3+……+n

3 ={

}

2 ,

→ n / 12+2

2+3

2+4

2+……+n

2 =

( )

Type 1 : → 2-5-12-19-….. ?

Type 2 : → 5+8+11+14+….. 383 ?

→ 8+11+14+17+…… 392 ?

→ 4+7+10+13+…. 301 ?

Type 3 :→ 1+2+3+4+….+99 = ?

→ 5+11+17+23+……+59 = ?

→ 29+25+21+…..-23 = ?

→ , 1+3+5+7+….+125 = 169+171+173+….+209.

Type 4 : → 1+3+5+7+….. n ?

→ 8+16+24+…. 9 ?

→ 11+18+25+32+…... 29 ?




→ 7+12+17+…… 30 ?

→ 12 77 , 23 ?

→ 16 -20 , 31 ?

→ n n(n+1) , ?

→ n n(n+1) , 10

?

→ + + +…… 10 ?

Type 5 : → P P2

q q2 , (p+q)

?

→ m n

n m , (m+n)

?

Type 6 : → 12 144 20 560 ,

6 ?

→ m n n m , (m+n)

?

Type 7 : → 9+7+5+….. n -144 , n

?

→ 2+4+6+8+.... n 2550 , n ?

Type 8 : → P , q r a,b,c ,

a(q-r)+b(r-p)+c(p-q) = 0

→ 2500

2 1 ,

?

→ 2000 ,

,

? %

?

Type Last : → Proved that, Sn =

{2a+(n-1)d}




Answer :

Type 1 : (1) -7, -75

Type 2 : (1) 100 (2) 127 (3) 129 (4) 100

Type 3 : (1) 4950 (2) 320 (3) 42

Type 4 : (1) n2

(2) 360 (3) 3161 (4) 2385 (5) 1771 (6) -620 (7) 2+4+6+….. (8) 2+4+6+….. ,

110 (9) 55

Type 5 : (1) P2+pq+q

2 (2) 0

Type 6 : (1) 0 (2) –(m+n)

Type 7 : (1) 18 (2) 50

Type 8 : (2) 50 (3) 11500 , 583940

( )

Type 1 : → 128+64+32+…. ?

→ 4+12+36+…… ?

→ 64+32+16+8+…… 8 ?

→ 128+64+32+…. ?

→ 2+4+8+16+….. 10 ?

Type 2 : → 128+64+32+….

?

→

-1+ - ……

?

→

, -1, , ……

?

Type 3 : → 12+24+48+….+768 = ?

→ 6+12+24+……+384 = ?

Type 4 : → 1+

+

+

+……. 5 ?

→ 1+

+

+

+……. 8 ?

→ 2+6+18+…… 8 ?

→ 2-4+8-16+…… 7 ?

→ 3-6+12+…… 10 ?

→ 3+9+27+…… 14 ?

→ + + +…… 12 ?

Type 5 : → 27 9 ,

?

→ 125 25 ,

?




→

,

?

→ 5 + x + y + 135 , x y ?

→ 3 + x + y + z + 243 , x , y z ?

Type 6 : → 1-1+1-1+…… (2n+1) ?

→ 2-2+2-2+……+…… (2n+2) ?

Type 7 : → 2+4+8+16+…… n 254 , n

?

Type 8 : → 10

10 ,

?

Type 9 : → n 441 , n

?

→ n 225 , n

?

→

= 210 , n ?

→ , 13+2

3+3

3+…..+10

3 = ( 1+2+3+….+10)

2

Type Last : → ?

→ n ?

→ n ?

→ n ?

Answer :

Type 1 : (1)

(2) 3, 8784 (3)

(4)

(5) 1024

Type 2 : (1) 9 (2) 9 (3) 9

Type 3 : (1) 1524 (2) 762

Type 4 : (1)

(2) 1

(3) 6560 (4) 86 (5) -1023 (6)

(7) 650

Type 5 : (1)

(2)

(3)

(4) x = 15, y = 45 (5) x = 9, y = 27, z = 81

Type 6 : (1) 1 (2) 0

Type 7 : (1) 7

Type 8 : (1) 24.47 . .( )

Type 9 : (1) 6, 21 (2) 5, 55 (3) 20




( ) 1200

100 । ( ) n ?

( ) n ?

( ) n ?

( ) ?

( ) n 2n-4

( ) ?

( ) 10 20 ?

( )

8 ?

( ) a, , - …

( ) ?

( ) ?

( ) ?




Youtube Chennal Link :

https://www.youtube.com/channel/UCpzRPfislF-

T1j1027FMyNQ

You can get Allah by having trust but

with critism you can’t get him…..Mind it….

That’s all for the time being………

https://www.youtube.com/channel/UCpzRPfislF-T1j1027FMyNQ

https://www.youtube.com/channel/UCpzRPfislF-T1j1027FMyNQ

jewel’s carejewelscare.weebly.com/uploads/1/1/0/7/110728531/ssc_sosimdhara_2017_page.pdfjewel’s...

Documents