Prove that for all positive integers n, 2'x1+2?x 2 + 2³x 3 + ... + 2" x n = 2+(n– 1)2"+1 Tips and Hints: • Towards the end it might help to remember that when you multiply, if the bases are the same, you can add the exponents x * x² = xY+Z. You might also find it helpful to remember that x can also be written as x' Example that applies both of these concepts: 2× + 2× = 2(2*) = 21 (2×) = 2×+1 • To avoid mistakes, don't forget to use parentheses and think about order of operations. Write clearly and don't take shortcuts.

Prove that for all positive integers n, 2'x1+2?x 2 + 2³x 3 + ... + 2" x n = 2+(n– 1)2"+1 Tips and Hints: • Towards the end it might help to remember that when you multiply, if the bases are the same, you can add the exponents x * x² = xY+Z. You might also find it helpful to remember that x can also be written as x' Example that applies both of these concepts: 2× + 2× = 2(2*) = 21 (2×) = 2×+1 • To avoid mistakes, don't forget to use parentheses and think about order of operations. Write clearly and don't take shortcuts.

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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