rove by induction that for all n ∈ N,5 + 7 + . . . + (2n + 3)= ∑i=ni=1 (2i + 3) = n(n + 4)

Question

rove by induction that for all n ∈ N,5 + 7 + . . . + (2n + 3)= ∑i=ni=1 (2i + 3) = n(n + 4)
🧐 Not the exact question you are looking for?Go ask a question

Solution 1

Sure, let's prove this by induction.

Step 1: Base Case Let's start with n=1. The left side of the equation becomes 21 + 3 = 5. The right side of the equation becomes 1(1+4) = 5. Since both sides are equal, the base case holds true.

Step 2: Inductive Step Assume the statement is true for some k ∈ Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

This problem has been solved

Similar Questions

rove by induction that for all n ∈ N,5 + 7 + . . . + (2n + 3)= ∑i=ni=1 (2i + 3) = n(n + 4)

All the following sequences converge to 1 except ..........*1 pointv_n={ n/(2n+1) }u_n={ 2n/(2n+1) }w_n={ (1+n)/(7+n) }z_n={ (n+3)/(n+4) }

If a = 2 + i, and b =  3 – 2i, what is b/a?Question 3Select one:a.4/5 -(7/5)ib.2 + (1/5)ic.10 – id.10 + ie.Impossible

12.Find ∫ x2 − 2x dx 52using First Principles. (Ans: 18)Hint: ∑ 1 =ni=1 n, ∑ i =n(n+1)2,ni=1 ∑ i2 =n(n+1)(2n+1)6

Prove by mathematical induction that11×2×3+12×3×4+ ⋯ +1n(n+1)(n+2)=14−12(n+1)(n+2).

1/3