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hushjelpw4

hushjelpw4

Answered question

2022-05-21

6 4 × 2 + 7 5 × 2 + . . . + 21 19 × 2
I got this exercise from school and I have no idea what notion to use, it resumes to Harmonic series, I can't find a generic answer. Do you have any idea?
6 4 × 2 + 7 5 × 2 + . . . + 21 19 × 2
Which is the generic answer for such a sum?

Answer & Explanation

Harley Fitzpatrick

Harley Fitzpatrick

Beginner2022-05-22Added 13 answers

Consider the most general case
A = i = a b n 2 ( n 2 ) = 1 2 i = a b n n 2 = 1 2 i = a b n 2 + 2 n 2
A = 1 2 i = a b 1 + i = a b 1 n 2 = ( b a + 1 ) + i = a b 1 n 2
So, you are just left with the sum of fractions 1 4 + 1 5 + 1 6 + + 1 19
Anthony Kramer

Anthony Kramer

Beginner2022-05-23Added 2 answers

We got the following sum:
n = 6 21 n 2 ( n 2 ) =
6 2 ( 6 2 ) + 7 2 ( 7 2 ) + 8 2 ( 8 2 ) + 9 2 ( 9 2 ) + . . . + 21 2 ( 21 2 ) =
6 8 + 7 10 + 8 12 + 9 14 + . . . + 21 38 =
753813839 77597520

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