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Find the sum of the infinite series 1+...

Find the sum of the infinite series
`1+(1)/(3)+(1.3)/(3.6)+(1.3.5)/(3.6.9)+…..`

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Find the sum of the infinite series (3)/(4)+(3.5)/(4.8)+(3.5.7)/(4.8.12)+….

Find the sum of the infinite series (3)/(4)+(3.5)/(4.8)+(3.5.7)/(4.8.12)+....

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

(1.3)/(3.6)+(1.3.5)/(3.6.9)+(1.3.5.7)/(3.6.9.12)+…=

Find the sum of the infinite series (3)/(4.8)-(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)-......

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If x=(1)/(3)+(1.3)/(3.6)+(1.3.5)/(3.6.9)+…. , then x^2+2x-2=

1+(1)/(2!)+(1.3)/(4!)+(1.3.5)/(6!)+...=

Show that 1 + 1/3 + (1.3)/(3.6) + (1.3.5)/(3.6.9) + ….. = sqrt3