sum _(i=1)^100i^2=1^2+2^2+3^2+ldots +100^2 infty 383350 338530 338350 333850

## Step 1: Identify the type of series<br />### The given series is a finite series because the upper limit of the summation is a finite number (100).<br /><br />## Step 2: Recognize the sum of squares formula<br />### The series represents the sum of squares of the first 100 natural numbers. The formula for the sum of squares of the first $n$ natural numbers is given by:<br />$S_n = \frac{n(n+1)(2n+1)}{6}$.<br /><br />## Step 3: Apply the formula<br />### Substitute $n = 100$ into the formula:<br />$S_{100} = \frac{100(100+1)(2(100)+1)}{6} = \frac{100 \cdot 101 \cdot 201}{6}$.<br /><br />## Step 4: Calculate the sum<br />### $S_{100} = \frac{2030100}{6} = 338350$.