Question

Explain how he might have used the Sn formula to get his result.

Answer 1

i can prove that ... without using Sn

Answer 2

1 + 2 + 3 + ... + 100
100 + 99 + 98 + ... + 1
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101 + 101 + 101 ..... + 101

so you have 100*101. divide that by 2 to get your answer...

Answer 3

exactly as @dpaInc

Answer 4

because you have 100 of those 101...

Answer 5

let x = 1 + 2 + 3 + ... + 100
so
1 + 2 + 3 + ... + 100 = x
100 + 99 + 98 + ... 1 = x
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101+ 101 +101...+101 = 2x

101*100 = 2x
so x = 100*101/2 = 50*101