Which of the following statement is correct?

I. The value of 100² - 99² + 98² - 97² + 96² - 95² + 94² - 93² + ...... + 22² - 21² is 4840.

II. The value of 

\(\rm \left( {{k^2}+\frac{1}{{{k^2}}}} \right)\left( {k - \frac{1}{k}} \right)\left( {{k^4}+\frac{1}{{{k^4}}}} \right)\left( {k+\frac{1}{k}} \right)\left( {{k^4}-\frac{1}{{{k^4}}}} \right)\) is k¹⁶ - \(\frac{1}{k^{16}}\).

Given:

I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 is 4840.

II. The value of 

\(\rm \left( {{k^2}+\frac{1}{{{k^2}}}} \right)\left( {k - \frac{1}{k}} \right)\left( {{k^4}+\frac{1}{{{k^4}}}} \right)\left( {k+\frac{1}{k}} \right)\left( {{k^4}-\frac{1}{{{k^4}}}} \right)\) is k16 - \(\frac{1}{k^{16}}\).

Concept used:

A, (A + D), (A + 2D), ....., L is an arithmetic progression with the first term A and common difference D. (L being the N^th term)

Number of terms, N = (L - A)/D + 1

Sum of all terms = (A + L)/2 × N

Calculation:

II. ​According to the concept,

1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212

(100 + 99)(100 - 99) + (98 + 97)(98 - 97)+...........(22 + 21)(22 - 21)

So, the series will be

100 + 99 + 98 + 97 .............................................22 + 21.

The first term is 100 and the last is 21, the difference is 1.

Sum = (100 + 21) × 80/2 = 121 × 40 = 4840

II. \(\rm \left( {{k^2}+\frac{1}{{{k^2}}}} \right)\left( {k - \frac{1}{k}} \right)\left( {{k^4}+\frac{1}{{{k^4}}}} \right)\left( {k+\frac{1}{k}} \right)\left( {{k^4}-\frac{1}{{{k^4}}}} \right)\)

⇒ \((k + \frac {1}{k}) (k - \frac {1}{k}) (k^2 + \frac {1}{k^2}) (k^4 + \frac {1}{k^4}) (k^4 - \frac {1}{k^4})\)

⇒ \((k^2 - \frac {1}{k^2}) (k^2 + \frac {1}{k^2}) (k^4 + \frac {1}{k^4}) (k^4 - \frac {1}{k^4})\)

⇒ \((k^4 - \frac {1}{k^4}) (k^4 + \frac {1}{k^4}) (k^4 - \frac {1}{k^4})\)

⇒ \((k^{8} - \frac {1}{k^{8}}) (k^4 - \frac {1}{k^4})\) ≠ \((k^{16} - \frac {1}{k^{16}}) \)

∴ Only I is true.