Arithmetic and Geometric Series Proofs (sn)

snowdrift
ARITHMETIC SERIES

Prove where Tn =
at Cn -
not



" "

let the first term of an arithmetic be and the constant
" "
sequence a

difference be d

• : Sn =
at la +
d) + ( a -12 d) + . .
. -1 Tn Where Tn =
attn -


1) d


Sn = a + ( atd ) + (at 2d ) +
. . .
+ (Tn -

2.d) 1- (Tn d) + Tn
-




Sn = Tn + (Tn d) -
+ ( Tn -
2. d) +
. . . + la -12 d) + (atd ) +a




•
: Zsn = (Attn) -1
(attn) + (attn) -1
. . .
1- (attn) -1 ( attn ) -1 (attn)
a


•
: Zsn =
n ( Attn)


Sn (attn) define Tn
2-
: = •

must
•
at least 3 terms on either side

but Tn =
a + Cn Dd
-
•
Learn



: Sn =-3 [ atatln Dd] -




Sn
2- [ zatln Dd]
: = -