[" ries : "],[" 1.(i) "1+(3)/(2)+(5)/(2^(2))+(7)/(2^(3))+....]

Find the sum to n terms of the following (1-2) series: (i) 1+3/2+5/(2^(2))+7/(2^(3))+ ………….. (ii) 1+2/3+3/(3^(2))+4/(3^(3))+ …………

Statement-I : (1)/(1.2)+(1)/(2.2^(2))+(1)/(3.2^(3))+….oo=log_(e )1//2 Statement-II : ((1)/(5)+(1)/(7))+(1)/(3)((1)/(5^(3))+(1)/(7^(3)))+(1)/(5)((1)/(5^(5))+(1)/(7^(5)))+….+oo=(1)/(2)log2 Which of the above is true

Statement-I : (1)/(1.2)+(1)/(2.2^(2))+(1)/(3.2^(3))+….oo=log_(e )1//2 Statement-II : ((1)/(5)+(1)/(7))+(1)/(3)((1)/(5^(3))+(1)/(7^(3)))+(1)/(5)((1)/(5^(5))+(1)/(7^(5)))+….+oo=(1)/(2)log2 Which of the above is true

Verify the following: (i) ((3)/(4)+(-2)/(5))+(-7)/(10)=(3)/(4)+((-2)/(5)+(-7)/(10)) (ii) ((-7)/(11)+(2)/(-5))+(-13)/(22)=(-7)/(11)+((2)/(-5)+(-13)/(22)) (iii) -1+((-2)/(3)+(-3)/(4))=(-1+(-2)/(3))+(-3)/(4)

Perform the indicated operations and write the result in the form x+iy: (i) (-3+2i)+(-6+3i) (ii) ((1)/(2)+(7)/(2)i)-(4+(5)/(2)i) (iii) (1-2i)-i+(4-7i)-2i+(5i+3) .

1 Simplify: (i) 2^((2)/(3)) times 2^((1)/(5) and ((1)/(3)^(3))^(7)

Simplify : (i) 2^(2//3).2^(1//5) (ii) ((1)/(3^(3)))^(7) (iii) (11^((1)/(2)))/(11^((1)/(4))) (iv) 7^(1//2).8^(1//2)

Simplify ( i ) (((1)/(3))^(-2)-((1)/(2))^(-3)}-:((1)/(4))^(-2)*( ii) ((5)/(8))^(-7)xx((8)/(5))^(-5)

Find a rational number between : (i)(3)/(7)and(5)/(14)""(ii)(2)/(5)and-(1)/(3)""(iii)-(1)/(3)and-(1)/(2)

Find a rational number between : (i)(3)/(7)and(5)/(14)""(ii)(2)/(5)and-(1)/(3)""(iii)-(1)/(3)and-(1)/(2)