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Unformatted text preview: Example: the sequence { 1 , 3 , 5 , 7 , 9 , . . . } = { 1 + 2 n, n = 0 , 1 , 2 , . . . , } . 4. Summation: a m + a m +1 + + a n = n s j = m a j Examples, 5 s j =1 j 2 = s s { , 2 , 4 } s 2 = 5. The sum of terms of a geometric progression is given by S n = n s j =0 ar j = a ( r n +11) r1 if r n = 1 ( n + 1) a if r = 1 6. Two frequently used summation formulae n s j =1 j = n ( n + 1) 2 n s j =1 j 2 = n ( n + 1)(2 n + 1) 6 We will prove these identities by mathematical induction later. 7. Question: the sum of terms of arithmetic progression is given by A n = n s j =0 ( a + jd ) = 1...
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 Winter '08
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