Use mathematical induction to prove that2² x 5+5² x 8+8² × 11for n=1,2,....+...+(3n-1)²(3n+2)== n(3n-1)(3n+2) (3n + 5)

We have to prove that 22×5+52×8+82×11+········+3n-123n+2=14n(3n-1)(3n+2)(3n+5) By using…

Answered: Use mathematical induction to prove…

Use mathematical induction to prove that 22 x 5+5² x 8+8² x 11+...+(3n-1)²(3n+2) for n=1,2,.... = n(3n-1) (3n+2) (3n+ 5)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.5: Mathematical Induction

Problem 32E: Prove by induction that 1+2n3n for n1.

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Question

Use mathematical induction to prove that
2² x 5+5² x 8+8² × 11
for n=1,2,....
+...+(3n-1)²(3n+2)
=
= n(3n-1)(3n+2) (3n + 5)

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