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Re: The sequence S1, S2, S3..., Sn ... is such that Sn= 1/n - 1/(n+1). If [#permalink]
12 Jul 2011, 12:51
First see the sum of first 3 terms: (1 - 1/2) + (1/2 - 1/3 ) + (1/3 - 1/4) = 3/4 similarly first sum of first 2 terms: 2/3 therefore it will be of the form, sum of first n terms = n/n+1 since this is a proper fraction, adding one to Numerator and denominator increases the overall value. consider stmt 1: k > 10; the sum of first 10 terms is = 10/11 which is (9+1)/(10+1) that means greater than 9/10.
but in stmt 2: sum of fist 9 (or fewer terms) is less than 9/10 and sum of terms more than 9 is greater than 9/10.