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1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(...

`1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=`

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(1+1/3.(1)/(2^(2))+1/5.(1)/(2^(4))+1/7(1)/2^(6)+…..oo) =

(1+1/3.(1)/(2^(2))+1/5.(1)/(2^(4))+1/7(1)/2^(6)+…..oo) =

The sum of the series 1 + (1)/(3^(2)) + (1 *4)/(1*2) (1)/(3^(4))+( 1 * 4 * 7)/(1 *2*3)(1)/(3^(6)) + ..., is (a) ((3)/(2))^((1)/(3)) (b) ((5)/(4))^((1)/(3)) (c) ((3)/(2))^((1)/(6)) (d) None of these

(1)/(2)((1)/(5)+(1)/(7))-(1)/(4)((1)/(5^(2))+(1)/(7^(2)))+(1)/(6)((1)/(5^(3))+(1)/(7^(3)))-….oo=

(1)/(2)((1)/(5)+(1)/(7))-(1)/(4)((1)/(5^(2))+(1)/(7^(2)))+(1)/(6)((1)/(5^(3))+(1)/(7^(3)))-….oo=

(1)/(2.3)+(1)/(4.5)+(1)/(6.7)+……oo=

Using appropriate properties find : (2)/(5) xx ((-3)/(7)) - (1)/(6) xx (3)/(2) + (1)/(14) xx (2)/(5) = (2)/(5) xx ((-3)/(7)) + (1)/(14) xx (2)/(5) - (1)/(cancel6) xx (cancel 3)/(2) = (2)/(5) xx ((-3)/(7) + (1)/(14) ) - (1)/(4) = (2)/(5) xx ((-6+1)/(14))- (1)/(4) = (cancel 2)/(cancel 5) xx (-cancel 5)/(cancel14) - (1)/(4) = (-1)/(7) - (1)/(4) (- 4 - 7)/(28) = (-11)/(28)

The greatest of the numbers 2(1)/(2),3^((1)/(3)),4^((1)/(4)),5^((1)/(5)),6^((1)/(6)) and 7^((1)/(7)) is