# Learn how to Calculate Sum / Summation of Series - Tutorial

## How to Calculate Sum / Summation of Series - Definition, Formula and Example

##### Definition:

A series denotes the sum of terms of a sequentially ordered finite or infinite set of term and summation denotes the process of totaling a series of numbers. The Finite sequences and series have first and last terms, whereas the infinite sequences and series continue indefinitely.

##### Formula: Where, n = Number of terms k = Number sequence
##### Example :

Find sum for the following series Number of terms = 5

##### Given,

Number of terms (n) = 5 Number sequence (k) = 1, 2...5

##### To Find,

Sum of Series : ∑k , ∑k2, ∑k3, ∑(k(k+1)), ∑(1/(k(k+1))), ∑(k(k+1)(k+2)), ∑(1/(k(k+1)(k+2))), ∑(2k - 1)

##### Solution:

Let us calculate the summation for the given series,

##### Step 1:

∑k = (5 x (5+1)) / 2 ∑k = 15

##### Step 2:

∑k2 = (5 x (5+1) x ((2 x 5)+1)) / 6 ∑k2 = 55

##### Step 3:

∑k3 = (52 x (5+1)2) / 4 ∑k3 = 225

##### Step 4:

∑(k(k+1)) = (5 x (5+1) x (5+2)) / 3

∑(k(k+1)) = 70

##### Step 5:

∑(1/(k(k+1))) = 5 / (5+1) ∑(1/(k(k+1))) = 0.8333

##### Step 6:

∑(k(k+1)(k+2)) = (5 x (5+1) x (5+2) x (5+3)) / 4 ∑(k(k+1)(k+2)) = 420

##### Step 7:

∑(1/(k(k+1)(k+2))) = 5 x (5+3) / 4 x (5+1) x (5+2) ∑(1/(k(k+1)(k+2))) = 0.23809

##### Step 8:

∑(2k - 1) = 52 ∑(2k - 1) = 25 Hence, the summation values for the given series are calculated.