Page 8 - Math Grade 11 (Advance)

PROEUS DARA

- = ---
1 . 2 1 2
1 1 1
2·3=2-3

1 - 1 1
3·4_3_4

1 1
(n- l). n = n- 1 - n

1
n. (n + 1) = n- n + 1
1
Un»t!Sti»tl ttHil2 S = 1---
u A A n+l
1
1
1
n
ctnmsg - 1 +- +- + ... + 1 = 1- -- = --
1 1·2 2·3 3·4 n·(n+l) n+l n+l
0 • 0
ru'UlHlf!U
u
ac~ru tf:lrotHi ru1 2ld rulJn&s g tt!lliHLli ro'l§.nH1

4 4 3 2
(k+1) -k = 4k +6k +4k+l tt!lru2J k t:lru n
2
3
4
4
2 - 1 = 4 X 1 + 6 X 1 + 4 X 1 + 1

4 4 3 2
n -(n-1) =4x(n-1) +6x(n-l) +4x(n-l)+l
4 4 3 2
(n + 1) - n = 4 x n + 6 x n + 4 x n + 1
4 4 3 3 3 3 2 2 2 2
(n + 1) - 1 = 4 x ( 1 + 2 + 3 + ... + n ) + 6 x (1 + 2 + 3 + ... + n )
+ 4 x (I+ 2 + 3 + ... + n) + (1 + l + 1 + ... + 1)
2 2 2 2
= 4S + 6 X ( 1 + 2 + 3 + ... + n ) + 4 X ( 1 + 2 + 3 + ... + n) + ( 1 + 1 + 1 + ... + l)

f:lrul2l s tf:ltil2 13+23+33+ ... +n3 = n2(n4+1)2 = [n(n2+l)r

1 1 1 1
s = -- + -- + -- + ... + -..,---,..--,..---
1·2·3 2·3·4 3·4·5 n·(n+l)·(n+2)

3