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From: raghu@fshvmfk1.vnet.ibm.com
Newsgroups: comp.theory
Subject: Re: expression for F(n) = a**0 + a**1 + ... + a**n
Message-ID: <9106190652.AA05711@ucbvax.Berkeley.EDU>
Date: 18 Jun 91 12:16:52 GMT
Sender: daemon@ucbvax.BERKELEY.EDU
Lines: 31


 >Subject: expression for F(n) = a**0 + a**1 + ... + a**(n-1) + a**n
 >From: ping@bnlux1.bnl.gov (Shiping Zhang)
 >Message-ID: <1991Jun18.022651.16732@bnlux1.bnl.gov>
 >Date: 18 Jun 91 02:26:51 GMT
 >
 >I'm wondering if there is an expression for F(n) = a**0 + a**1 + ... +a**n
 >in term of both a and n. Here a is a constant. I know the expression fr
 >a = 2, which is 2**(n+1) -1.  But now I want to know the expression fo
 >any constant a.  Thanks for any help.
 >
 >-ping

     F(n) is a geometric series, where the ith term is given by the
     the recurrence relation :
                   T(i) = r*T(i-1)
     r is called the common ratio.  The sum of n terms is

                    T(0) * (r**n - 1) / (r - 1)

     In your case T(0) = 1, r = a, n = n+1, so the sum is
                      (r**(n+1) - 1) / (r -1). If r = a = 2, the sum is
     is the same as the one you have.


 Raghu V. Hudli
 IBM Corp

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