Let P(n) be the statement that 12+22+.+n²= n(n+1)(2n +1) for n =1, 2, ... Which of the 6. following statements is P(1)? 1(1+1)(2+1) O 1²=. 6. 0(0 +1)(0 +1) 02- 6. o 12+22+. +n²=. n(n +1)(2n +1) 6. On=1
Let P(n) be the statement that 12+22+.+n²= n(n+1)(2n +1) for n =1, 2, ... Which of the 6. following statements is P(1)? 1(1+1)(2+1) O 1²=. 6. 0(0 +1)(0 +1) 02- 6. o 12+22+. +n²=. n(n +1)(2n +1) 6. On=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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![**Question 1**
Let \( P(n) \) be the statement that
\[ 1^2 + 2^2 + \ldots + n^2 = \frac{n(n+1)(2n+1)}{6} \]
for \( n = 1, 2, \ldots \). Which of the following statements is \( P(1) \)?
- \(\bigcirc \; 1^2 = \frac{1(1+1)(2+1)}{6}\)
- \(\bigcirc \; 0^2 = \frac{0(0+1)(0+1)}{6}\)
- \(\bigcirc \; 1^2 + 2^2 + \ldots + n^2 = \frac{n(n+1)(2n+1)}{6}\)
- \(\bigcirc \; n = 1\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79599c56-a340-49a0-b0ff-829b3947a798%2Ffe368f1e-36c0-4de0-9690-86883d1fa3f7%2Fzza4znb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 1**
Let \( P(n) \) be the statement that
\[ 1^2 + 2^2 + \ldots + n^2 = \frac{n(n+1)(2n+1)}{6} \]
for \( n = 1, 2, \ldots \). Which of the following statements is \( P(1) \)?
- \(\bigcirc \; 1^2 = \frac{1(1+1)(2+1)}{6}\)
- \(\bigcirc \; 0^2 = \frac{0(0+1)(0+1)}{6}\)
- \(\bigcirc \; 1^2 + 2^2 + \ldots + n^2 = \frac{n(n+1)(2n+1)}{6}\)
- \(\bigcirc \; n = 1\)
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