Find the right part of the equality. $1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } + \ldots + n ^ { 2 } =$________

A) $\frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 }$
B) $\frac { n ( n + 1 ) ( n + 3 ) } { 4 }$
C) $\frac { n ( n + 1 ) } { 2 }$
D) $\frac { ( n + 1 ) ( n + 2 ) } { 3 }$
E) none of the above

Question

Find the right part of the equality. $1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } + \ldots + n ^ { 2 } =$________

A) $\frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 }$
B) $\frac { n ( n + 1 ) ( n + 3 ) } { 4 }$
C) $\frac { n ( n + 1 ) } { 2 }$
D) $\frac { ( n + 1 ) ( n + 2 ) } { 3 }$
E) none of the above

Quizplus · Accepted Answer

This is the formula for the sum of the first n perfect squares, known as the "square pyramidal number formula." It can be derived using mathematical induction or by using the formula for the sum of consecutive integers and the formula for the sum of consecutive squares. The other answer choices are formulas for the sum of consecutive integers or other sequences, and do not apply to this problem.

Find the Right Part of the Equality 12+22+32+…+n2=1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } + \ldots + n ^ { 2 } =12+22+32+…+n2=

Find the Right Part of the Equality $1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 2 } + \ldots + n ^ { 2 } =$