Which of the following statement is correct? I. The value of 1002 - 9…

Question

Which of the following statement is correct?
I. The value of 100² - 99² + 98² - 97² + 96² - 95² + 94² - 93² + . . . . + 2² - 1² is 5050.
II. If 8x +

\frac{8}{x}

= -16 and x < 0, then the value of x¹⁹⁷ + x^-197 is 2.

Accepted Answer

Option A. Only I. Answer & Solution Answer: Option A Solution: I. 100 2 − 99 2 ⎵ + 98 2 − 97 2 + . . . .+ 2 2 − 1 2 & = ( 100 + 99 ) ( 100 - 99 ) + ( 98 + 97 ) ( 98 - 97 ) + ( 96 + 95 ) ( 96 - 95 ) + \,.\,.\,.\,.\, + ( 2 + 1 ) ( 2 - 1 ) & n ( n + 1 )2 = sum of n terms & = 100 × 1012 & = 5050 & St…

Which of the following statement is correct? I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + . . . . + 22 - 12 is 5050. II. If 8x + 8 x = -16 and x < 0, then the value of x197 + x-197 is 2.

Solution