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निम्न श्रेणी का अनंत तक योग ज्ञात कीजिए|...

निम्न श्रेणी का अनंत तक योग ज्ञात कीजिए|
` 1+ ( 2)/(3) .(1)/(2) +(2.5)/( 3.6) .(1)/(2^(2) )+( 2.5.8)/( 3.6.9) .(1)/( 2^(3))+........`

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Show that 1 + 2/3.1/2 + (2.5)/(3.6) (1/2)^2 + (2.5.8)/(3.6.9) (1/2)^3 + ….. = root(3)4

Prove that : Find the sum of the infinite series 1+(2)/(3).(1)/(2)+(2.5)/(3.6)((1)/(2))^(2)+(2.5.8)/(3.6.9)((1)/(2))^(3)+......oo

Prove that : Find the sum of the infinite series 1+(2)/(3).(1)/(2)+(2.5)/(3.6)((1)/(2))^(2)+(2.5.8)/(3.6.9)((1)/(2))^(3)+......oo

1+(2)/(3)xx(1)/(2)+(2)/(3)xx(5)/(6)xx(1)/(2^(2))+(2)/(3)xx(5)/(6)xx(8)/(9)xx(8)/(9)xx(1)/(2^(3))+...oo

1+((1)/(2)+(1)/(3))/((1)/(3)-(1)/(6))/2-((4)/(5)of(5)/(6))/((2)/(3))

Q.the sum of the infinite series 1+(2)/(3)*(1)/(2)+(2)/(3)*(5)/(6)*(1)/(2^(2))+(5)/(3)*(5)/(6)*(8)/(9)*(1)/(2^(3))+... is

(5)/(6) -: (6)/(7) xx ? - (8)/(9) -: 1 (2)/(5) -: (3)/(4) xx 3 (1)/(3) = 2(7)/(9)

1(5)/(6)+[2(2)/(3)-{3(3)/(4)(3(4)/(5)-:9(1)/(2))}]

5(5)/(6) + [2(2)/(3) - [3(3)/(4) (3(4)/(5) div 9(1)/(2))]]