Prove that the ratio of the sum of odd terms, Mathematics

If there are (2n+1)terms  in an AP ,prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n

Ans:    Let a, d be the I term & Cd of the AP.

∴ ak = a + (k - 1) d

s1 = sum to odd terms

s1 = a1 +  a3 + ......... a 2n + 1

s1  = n +1/2 [a1 + a2 n +1 ]

= n + 1/2 [2a1 + 2nd]

s1 = (n + 1) (a + nd)

s2 = sum to even terms

s2 = a2 + a4 + ..... a 2n

s2  = n/2 [a2 + a2n  ]

= n/2 [a + d + a + (2n - 1)d]

=n [a + nd]

∴ s1 : s2 = (n +1)(a nd )/n(a nd )

= n+1/n

Posted Date: 4/8/2013 6:05:06 AM | Location : United States







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