An arithmetic series is the sum of all the terms of an arithmetic sequence. The two formulae derived in class are Sn = (t, + t,) and S, =[2a + (n – 1)d]. 1. a) Given S, = a + (a + d) + (a + 2d) + ..+ (t, – 2d) + (t, - d) + tn, derive the formula S, = (t, + t,) Sn = a + (a + d) + (a + 2d) + ·.+ (tn – 2d) + (tn – d) + tn ... b) Given S, =(t, + tn), derive the fomula S, =[2a + (n – 1)d]
An arithmetic series is the sum of all the terms of an arithmetic sequence. The two formulae derived in class are Sn = (t, + t,) and S, =[2a + (n – 1)d]. 1. a) Given S, = a + (a + d) + (a + 2d) + ..+ (t, – 2d) + (t, - d) + tn, derive the formula S, = (t, + t,) Sn = a + (a + d) + (a + 2d) + ·.+ (tn – 2d) + (tn – d) + tn ... b) Given S, =(t, + tn), derive the fomula S, =[2a + (n – 1)d]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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An arithmetic series is the sum of all the terms of an arithmetic sequence. The two formulae derived in class are
S, = (t, + t,) and S, = [2a + (n – 1)d].
a) Given S, = a + (a + d) + (a + 2d) + -
· + (tn – 2d) + (t, - d) + tn, derive the formula S, = " (t, + t,)
...
Sn 3а+ (а+d) + (а + 2d) +
...+ (tn - 2d) + (tn — d) + tn
b) Given S, =(t, + t„), derive the fomula S,
= [2a + (n – 1)d]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd36d9f14-85a6-44e8-8adb-3299969cf3e3%2Ffd091cb7-e4d0-4f31-a41b-83394d47937b%2Fud087ej_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
An arithmetic series is the sum of all the terms of an arithmetic sequence. The two formulae derived in class are
S, = (t, + t,) and S, = [2a + (n – 1)d].
a) Given S, = a + (a + d) + (a + 2d) + -
· + (tn – 2d) + (t, - d) + tn, derive the formula S, = " (t, + t,)
...
Sn 3а+ (а+d) + (а + 2d) +
...+ (tn - 2d) + (tn — d) + tn
b) Given S, =(t, + t„), derive the fomula S,
= [2a + (n – 1)d]
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