Why Is the Sum of 1/2 (n+1)/2?

  • Thread starter Thread starter theintarnets
  • Start date Start date
  • Tags Tags
    Sum
Click For Summary
SUMMARY

The summation of 1/2 from i = 0 to n results in (n+1)/2 due to the inclusion of the zero index, which adds an additional term to the total count. This means that the series has n+1 terms rather than n terms, leading to the final result of (n+1)/2 instead of n/2. Understanding this concept is crucial for accurately calculating sums in series where the index starts at zero.

PREREQUISITES
  • Basic understanding of summation notation
  • Familiarity with series and sequences
  • Knowledge of arithmetic operations
  • Concept of indexing in mathematical expressions
NEXT STEPS
  • Study the properties of summation notation in mathematics
  • Explore the concept of series convergence and divergence
  • Learn about different types of series, including geometric and arithmetic series
  • Investigate the implications of indexing in programming and algorithms
USEFUL FOR

Students of mathematics, educators teaching summation concepts, and anyone interested in understanding series calculations in mathematical contexts.

theintarnets
Messages
64
Reaction score
0
I don't understand why the answer to this summation:
n
Ʃ 1/2
i = 0

is (n+1)/2
Why isn't it just n/2?
 
Physics news on Phys.org
theintarnets said:
I don't understand why the answer to this summation:
n
Ʃ 1/2
i = 0

is (n+1)/2
Why isn't it just n/2?


Because the index starts at zero. 0,1,2,...n has n+1 terms.
 

Similar threads

Find the sum of the coefficients in the expansion ##(1+x)^n##
  • · Replies 5 ·
Replies
5
Views
2K
Trying to find an easier way to compute the double sum
  • · Replies 7 ·
Replies
7
Views
2K
Every integer greater than 5 is the sum of three primes?
  • · Replies 4 ·
Replies
4
Views
4K
Find the values of ## n\geq 1 ## for which ## 1+2+3+\dotsb +n ##.
  • · Replies 4 ·
Replies
4
Views
2K
Show that ##^{n+1}C_r=^nC_r+^nC_{r-1}##
  • · Replies 14 ·
Replies
14
Views
3K
Mathematical Induction with binomial sum
  • · Replies 9 ·
Replies
9
Views
4K
Show that the sum of twin primes ## p ## and ## p+2 ## is divisible?
  • · Replies 17 ·
Replies
17
Views
3K
Prove that ## a^{({2}^{n})}\equiv 1\pmod {2^{n+2}} ## for any ##n##?
  • · Replies 6 ·
Replies
6
Views
3K
Sum of Infinite Series: Finding the Value of S
  • · Replies 10 ·
Replies
10
Views
3K
Prove that there are infinitely many primes of the form ## 6k+1 ##?
  • · Replies 12 ·
Replies
12
Views
4K