summation formula explained Summation notation or sigma notation allows us to write a long sum in a single expression Unpacking the meaning of summation notation This is the sigma symbol It tells us that we are summing something Let s start with a basic example Stop at n 3 inclusive n 1 3 2 n 1 Expression for each Start at n 1 term in the sum
A summation has 4 key parts the upper bound the highest value the index variable will reach index variable variable that will change in each term of the summation the lower bound lowest value of the index value the one it starts at and an expression Applying Equation 9 2 begin array rcl 1 2 3 ldots n dfrac n n 1 2 end array nonumber So for example the sum of the first 100 natural numbers 5 is frac 100 101 2 5050 An important application of the geometric sum formula is the investment plan called an annuity
summation formula explained
summation formula explained
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M i nai an an 1 an 2 am 2 am 1 am i n m a i a n a n 1 a n 2 a m 2 a m 1 a m The i i is called the index of summation This notation tells us to add all the ai a i s up for all integers starting at n n and ending at m m For instance The following formula means to sum up the weights of the four grapes sum i 1 4 X i The Greek letter capital sigma sum indicates summation The i 1 at the bottom indicates that the summation is to start with X 1 and the 4 at the top indicates that the summation will end with X 4
We can square n each time and sum the result 4 n 1 n 2 1 2 2 2 3 2 4 2 30 We can add up the first four terms in the sequence 2n 1 4 n 1 2n 1 3 5 7 9 24 We can use other letters here we use i and sum up i i 1 going from 1 to 3 3 i 1 i i 1 1 2 2 3 3 4 20 Try writing out the sum rather than using summation notation When we get to mathematical induction in Section 4 2 it will be important that we can work with summations where we want to add the n 1 term to a summation
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23K 1 5M views 6 years ago New Calculus Video Playlist This calculus video tutorial provides a basic introduction into summation formulas and sigma notation It explains how to find the Here are the steps in detail for writing the sum of terms as summation notation Find the general term of the terms of the sum If the sequence of terms is arithmetic geometric then we can use the general term formula of the respective sequences If not we will find the general formula by investigation and observation
The n 1 is the lower bound of summation and the 5 is the upper bound of summation meaning that the index of summation starts out at 1 and stops when n equals 5 In the above example n is the expression Therefore to evaluate the summation above start at n 1 and evaluate the expression Summation notation uses the sigma symbol to represent sums with multiple terms See some more involved examples of how we read expressions in summation notation Questions Tips Thanks Want to join the conversation Log in Sort by Top Voted Swetha S 20 5 years ago Say you were given a series like 4 3 1 3 4
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