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Jewel’s Care Life is for motto lesson
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 : mdibrahimkhaliljewel@gmail.com
Demra, Dhaka - 1362
Jewel’s Care Life is for motto lesson
Jewel’s Care Life is for motto lesson
www.jewelscare.weebly.com Youtube Chennal Name : Jewel’s Care
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)
Jewel’s Care Life is for motto lesson
Jewel’s Care Life is for motto lesson
www.jewelscare.weebly.com Youtube Chennal Name : Jewel’s Care
→ 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 ?
Jewel’s Care Life is for motto lesson
Jewel’s Care Life is for motto lesson
www.jewelscare.weebly.com Youtube Chennal Name : Jewel’s Care
→ 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}
Jewel’s Care Life is for motto lesson
Jewel’s Care Life is for motto lesson
www.jewelscare.weebly.com Youtube Chennal Name : Jewel’s Care
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 ,
?
Jewel’s Care Life is for motto lesson
Jewel’s Care Life is for motto lesson
www.jewelscare.weebly.com Youtube Chennal Name : Jewel’s Care
→
,
?
→ 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
Jewel’s Care Life is for motto lesson
Jewel’s Care Life is for motto lesson
www.jewelscare.weebly.com Youtube Chennal Name : Jewel’s Care
( ) 1200
100 । ( ) n ?
( ) n ?
( ) n ?
( ) ?
( ) n 2n-4
( ) ?
( ) 10 20 ?
( )
8 ?
( ) a, , - …
( ) ?
( ) ?
( ) ?
Jewel’s Care Life is for motto lesson
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
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
Jewel’s Care Life is for motto lesson
www.jewelscare.weebly.com Youtube Chennal Name : Jewel’s Care
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………
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