Question

{[2^2×(1+2+.........+100)]:10100}^2013÷2^2013

Answer 1

={[4×(100×101)÷2]÷10100}^2013÷2^2013

=[(4×50×101)÷10100]^2013÷2^2013

=[(2×100×101)÷10100]^2013÷2^2013

=(2×10100÷10100)^2013÷2^2013

=2^2013÷2^2013

=1

Answer 2

{ [ 2² x ( 1 + 2 + 3 + ....... + 100 ) ] : 10 100 }²⁰¹³ : 2²⁰¹³ = 1

= { [ 4 x ( 100 × 101 : 2 ) ] : 10 100 }²⁰¹³ : 2²⁰¹³ =

= [ ( 4 × 5 050 ) : 10 100 ] ²⁰¹³ : 2²⁰¹³ =

= ( 20 200 : 10 100 ) ²⁰¹³ : 2²⁰¹³ =

= 2²⁰¹³ : 2²⁰¹³ =

= 2 ⁽ ²⁰¹³ ⁻ ²⁰¹³ ⁾ =

= 2⁰ =

= 1