This question shows a method to compute the sum of the first 100 natural numbers 100...

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This question shows a method to compute the sum of the first 100 natural numbers 100 n = 1 + 2 + 3 + 4 + + 99 + 100 n = 1 First write down the sum, then on the line below it write the sum backwards as shown 1 + 2 + 3 + 4 + + 99 + 100 100 99 +98 + 97 + + 2 + 1 Now add the two lines together (without a calculator). If you add vertically, something nice will happen allowing you to write the answer as a product of two numbers. 10100 Now use the above answer to find the original sum 100 n = 1 n = 5050 Generalize the above method to find a formula that computes the sum of the first N natural numbers N n = 1 n = n(n+1) 2 This question shows a method to compute the sum of the first 100 natural numbers 100 n = 1 + 2 + 3 + 4 + + 99 + 100 n = 1 First write down the sum, then on the line below it write the sum backwards as shown 1 + 2 + 3 + 4 + + 99 + 100 100 99 +98 + 97 + + 2 + 1 Now add the two lines together (without a calculator). If you add vertically, something nice will happen allowing you to write the answer as a product of two numbers. 10100 Now use the above answer to find the original sum 100 n = 1 n = 5050 Generalize the above method to find a formula that computes the sum of the first N natural numbers N n = 1 n = n(n+1) 2

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We need to find sum of n nu... View the full answer