Introduction to Telescoping Sum:
Telescoping sum is a summary property. Telescoping sum simplify our outline since it says that sum of a difference is equivalent to the final and initial term only, not depending on the center terms.
`sum_(i=1)^k` (ai+1 - ai) = ak+1 – a1
`sum_(i=1)^4` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)
= -a1+a5
= a5-a1
Examples for Telescoping sum:
Example 1 for Telescoping sum:
Deduce we have a series of numbers {1, 3, 9, 4, 2, 1} then we can place key on the series such that a1=1, a2=3,a3 = 9, a4 = 4, a56 = 1and we want to calculate the addition of variation = 2, a
`sum_(i=1)^5` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)
= (3-1)+(9-3)+(4-9)+(2-4)+(1-2)
= a6 - a1 = 1 - 1 = 0
Example 2 for Telescoping sum:
Deduce we have a series of numbers {1, 4, 16, 4, 2, 1} then we can place key on the series such that a1=1, a2=4, a3 = 16, a4 = 4, a5 = 2, a6 = 1and we want to calculate the addition of variation
`sum_(i=1)^5 ` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)
= (4-1) + (16-4) + (4-16) + (2-4) + (1-2)
= (3+12-12-2-1)
= a6 - a1 = 1 - 1 = 0
Example 3 for Telescoping sum:
Deduce we have a series of numbers {2, 3, 9, 4, 2, 2} then we can place key on the series such that a1=2, a2=3,a3 = 9, a4 = 4, a5 = 2, a6 = 2and we want to calculate the addition of variation
`sum_(i=1)^5` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)
= (3-2)+(9-3)+(4-9)+(2-4)+(2-2)
= a6 - a1 = 2 - 2 = 0
Example 4 for Telescoping sum:
Deduce we have a series of numbers {5, 3, 9, 4, 2, 5} then we can place key on the series such that a1=5, a2=3, a3 = 9, a4 = 4, a5 = 2, a6 = 5and we want to calculate the addition of variation
`sum_(i=1)^5` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)
= (3-5) + (9-3) + (4-9) + (2-4) + (5-2)
= a6 - a1 = 5 - 5 = 0
I like to share this gas density with you all through my article.
Telescoping sum is a summary property. Telescoping sum simplify our outline since it says that sum of a difference is equivalent to the final and initial term only, not depending on the center terms.
`sum_(i=1)^k` (ai+1 - ai) = ak+1 – a1
`sum_(i=1)^4` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)
= -a1+a5
= a5-a1
Examples for Telescoping sum:
Example 1 for Telescoping sum:
Deduce we have a series of numbers {1, 3, 9, 4, 2, 1} then we can place key on the series such that a1=1, a2=3,a3 = 9, a4 = 4, a56 = 1and we want to calculate the addition of variation = 2, a
`sum_(i=1)^5` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)
= (3-1)+(9-3)+(4-9)+(2-4)+(1-2)
= a6 - a1 = 1 - 1 = 0
Example 2 for Telescoping sum:
Deduce we have a series of numbers {1, 4, 16, 4, 2, 1} then we can place key on the series such that a1=1, a2=4, a3 = 16, a4 = 4, a5 = 2, a6 = 1and we want to calculate the addition of variation
`sum_(i=1)^5 ` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)
= (4-1) + (16-4) + (4-16) + (2-4) + (1-2)
= (3+12-12-2-1)
= a6 - a1 = 1 - 1 = 0
Example 3 for Telescoping sum:
Deduce we have a series of numbers {2, 3, 9, 4, 2, 2} then we can place key on the series such that a1=2, a2=3,a3 = 9, a4 = 4, a5 = 2, a6 = 2and we want to calculate the addition of variation
`sum_(i=1)^5` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)
= (3-2)+(9-3)+(4-9)+(2-4)+(2-2)
= a6 - a1 = 2 - 2 = 0
Example 4 for Telescoping sum:
Deduce we have a series of numbers {5, 3, 9, 4, 2, 5} then we can place key on the series such that a1=5, a2=3, a3 = 9, a4 = 4, a5 = 2, a6 = 5and we want to calculate the addition of variation
`sum_(i=1)^5` (ai+1 - ai) = (a2-a1)+(a3-a2)+(a4-a3)+(a5-a4)+(a6-a5)
= (3-5) + (9-3) + (4-9) + (2-4) + (5-2)
= a6 - a1 = 5 - 5 = 0
I like to share this gas density with you all through my article.