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Home Q & A Board Science-Related Homework Help Physics
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datageekgh datageekgh
wrote...
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11 years ago
I need to find a formula for 1+4+7+...+(3n-2) and prove it by induction. Help please!
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2 Replies
Replies
wrote...
#1
11 years ago
The sum is 3/2*n^2 - 1/2*n

Base, n = 1:
3/2*1^2 - 1/2*1 = 3/2 - 1/2 = 1

Step:  Assume that the formula is valid up to n.  For n+1, we thus have:
old sum + next number
= 3/2*n^2 -1/2*n + 3*(n+1) - 2
= 3/2*n^2 -1/2*n + 3*n + 3 - 2
= 3/2*n^2 -1/2*n + 3*n + 1
= 3/2*n^2 + 3*n + 3/2 - 1/2*n - 1/2
= 3/2*(n^2+2*n+1) - 1/2*(n+1)
= 3/2*(n+1)^2 - 1/2*(n+1)
Answer accepted by topic starter
DatchileDatchile
wrote...
#2
Posts: 109
Rep: 0 0
11 years ago
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