Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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1.7 Show that 1.8 Show that 1² +2²+ + n(n + 1) (2n + 1). 1³ + 2³ + ... + n³ = n²(n + 1)² . 1.9 Prove by induction the formula for the sum of an arithmetic series: a + (a + d) + (a + 2d) + + ½n(n − 1)d. +(a + (n − 1)d) = na + 1.10 Prove by induction the formula for the sum of a geometric series: a +ar+ar²+...+ ar-1 a(1-¹) 1-r (r = 1).
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Transcribed Image Text:1.7 Show that 1.8 Show that 1² +2²+ + n(n + 1) (2n + 1). 1³ + 2³ + ... + n³ = n²(n + 1)² . 1.9 Prove by induction the formula for the sum of an arithmetic series: a + (a + d) + (a + 2d) + + ½n(n − 1)d. +(a + (n − 1)d) = na + 1.10 Prove by induction the formula for the sum of a geometric series: a +ar+ar²+...+ ar-1 a(1-¹) 1-r (r = 1).
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