Question

Fain the value 1-2+3-4+5-6+7-8+9-10 up to 200 terms ans option -100 , -500, -200, -1000

Answer 1

1
$(1 + 3 + 5 + ....) - (2 - 4 - 6 - 8...) \\200 \div 2(399 = 3990 \\ 200 \div 2( - 2 +( - 396) = - 3960 \\ 3990 - 3960 = 30$

Answer 2

use ap..
first take the odd numbers i.e of 100terms
and even 100terms..
now addition of the succesive odd number from 1 gives u the square of the number of terms.i.e (100)²=10000
now even numbers are divisible by 2 thus 2(1+2+.....100)=11000. (use Sn=(100/2)(1+100))
now as even numbers are negative thus.
10000-11000=-100
thus option 1 is right