The value of _ x 0 2 ( 1- x 2 x [3] 3 x [10] 10 x x^2 ) is

Step-by-step solution

_ x 0 2 ( 1- (1- x^2 2 ! ) (1- 4 x^2 2 ! ) (1- 9 x^2 2 ! ) . (1- 100 x^2 2 ! ) x^2 ) By expansion gathered . _ x 0 2 (1- (1- x^2 2 ) ) (1- 1 2 4 x^2 2 ) (1- 1 3 9 x^2 2 ) . . (1- 1 10 100 x^2 2 ) x^2 ) _ x 0 2 ( .1- (1- x^2 2 ) (1- 2 x^2 2 ) (1- 3 x^2 2 ) . . (1- 10 x^2 2 ) ) x^2 ) _ x 0 2 (1-1+x^2 ( 1 2 + 2 2 + 3 2 + .+ 10 2 ) ) x^2 2 ( 1 2 + 2 2 + 3 2 + .+ 10 2 ) 1+2+ +10= 10 11 2 =55 gathered