Chapter 12.1, Problem 34E

To determine

Calculate the first six partial sums $S_1,S_2,S_3,S_4,S_5,S_6$ of the given sequence $1^2,2^2,3^2,4^2,\mathrm{......}$ .

Answer to Problem 34E

The sums of the first six partial sequence is $S_1=1,S_2=5,S_3=14,S_4=30,S_5=55,S_6=91$ .

Explanation of Solution

Given information:

It is given in the question that,

The sequence is $1^2,2^2,3^2,4^2,\mathrm{......}$ .

Formula used:

  $S_n=a_1+a_2+a_3+\mathrm{........}+a_n$ .

Calculation: The sequence is $1^2,2^2,3^2,4^2,5^2,6^2\mathrm{......}$ .

So,

  $\begin{array}{l}{S}_1=1^2=1\\ S_2=1^2+2^2=1+4=5\\ S_3=1^2+2^2+3^2=1+4+9=14\\ S_4=1^2+2^2+3^2+4^2=1+4+9+16=30\\ S_5=1^2+2^2+3^2+4^2+5^2=1+4+3+16+25=55\\ S_6=1^2+2^2+3^2+4^2+5^2+6^2=1+4+9+16+25+36=91\end{array}$

Finally, $S_1=1,S_2=5,S_3=14,S_4=30,S_5=55,S_6=91$ .