2n Using the expansion of (1 + x)² and given that 2nC₁ + 2(²nC₂) + 3(2n C3) + ... + 2n(2nC₂n) + 2n(²¹℃₂n) = n × 2²n Show that 2(²nC₁) + 3(²nC₂) + 4(²″C3) + ... + (2n + 1)(²nC₂n) = (n + 1) × 2²″ − 1
2n Using the expansion of (1 + x)² and given that 2nC₁ + 2(²nC₂) + 3(2n C3) + ... + 2n(2nC₂n) + 2n(²¹℃₂n) = n × 2²n Show that 2(²nC₁) + 3(²nC₂) + 4(²″C3) + ... + (2n + 1)(²nC₂n) = (n + 1) × 2²″ − 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2n
Using the expansion of (1 + x)²" and given that
211
²nC₁ + 2(²¹C₂) + 3(²¹℃3) + + 2n(²nC2n) = n × 2²m
Show that
1
2(²¹C₁) + 3(²¹C₂) + 4(²¹C3) + + (2n + 1)(²nC₂n) = (n + 1) × 2²n
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