Show that `(4.6)/(5.10) + (4.6.8)/(5.10.15) + (4.6.8.10)/(5.10.15.20) + ……. = 44/45`

Show that (3.5)/(5.10) + (3.5.7)/(5.10.15) + (3.5.7.9)/(5.10.15.20)+ …..oo = (5sqrt5)/(3 sqrt3) - 8/5

If t = 4/5 + (4.6)/(5.10) + (4.6.8)/(5.10.15) + ……oo then prove that 9t = 16

1-(1)/(5)+(1.4)/(5.10) - (1.5.7)/(5.10.15)+…..=

Find the sum of infinite terms of the series : (3)/(2.4) + (5)/(1.4.6) + (7)/(2.4.6.8)+ (9)/(2.4.6.8.10)+……

Convert the following into factorial. (i) 2.4.6.8.10.12.14.16.18.20 (ii) 1.3.5.7.9.11.13.15 (iii) 3.6.9.12.15 (iv) 6.7.8.9.10

Calculate the following a. (6.7 xx 10^(5)) xx (4.6 xx 10^(4)) b. (7.6 xx 10^(7)) xx (3.8 xx 10^(-4)) c. (6.8 xx 10^(-3)) xx (5.2 xx 10^(-4)) d. (6.7 xx 10^(5)) / (4.6 xx 10^(4)) e. (7.6 xx 10^(7)) / (3.8 xx 10^(-4)) f. (6.8 xx 10^(-3)) / (3.8 xx 10^(-4)) g. 7.65 xx 10^(2) + 2.72 xx 10^(3) h. 7.87 xx 10^(-4) - 2.61 xx 10^(-5)

Given x, y in R , x^(2) + y^(2) gt 0 . Then the range of (x^(2) + y^(2))/(x^(2) + xy + 4y^(2)) is (a) ((10 - 4 sqrt(5))/(3),(10 + 4 sqrt(5))/(3)) (b) ((10 - 4 sqrt(5))/(15),(10 + 4 sqrt(5))/(15)) (c) ((5- 4 sqrt(5))/(15),(5 + 4 sqrt(5))/(15)) (d) ((20- 4 sqrt(5))/(15),(20 + 4 sqrt(5))/(15))

Replace ( ) in each of the following by the correct number: (i) 2/7=6/((\ )) (ii) 5/8=(10)/((\ )) (iii) 4/5=((\ ))/(20) (iv) (45)/(60)=(15)/((\ )) (v) (18)/(24)=((\ ))/4

Solve for x: 4^(x+1.5) + 9^(x+0.5) = 10.6^x .

Which of the statement true ? 6:4.5 :: 4.8 : 3.6