For the series,
`S=1 +(1)/(1+3)(1+2)^2+(1)/((1+3+7))(1+2+3)^2+(1)/((1+3+5+7))(1+2+3+4)^2+...`

For the series S=1+(1)/((1+3))(1+2)^(2)+(1)/((1+3+5))(1+2+3)^(2)+(1)/((1+3+5+7))(1+2+3+4)^(2)+…………….., if the 7^("th") term is K, then (K)/(4) is equal to

For the series S=1+(1)/((1+3))(1+2)^(2)+(1)/((1+3+5))(1+2+3)^(2)+(1)/((1+3+5+7))(1+2_3+4)^(2)+…………….., if the 7^("th") term is K, then (K)/(4) is equal to

For the series S=1+(1)/((1+3))(1+2)^(2)+(1)/((1+3+5))(1+2+3)^(2)+(1)/((1+3+5+7))(1+2+3+4)^(2)+……….., if the sum of the first 10 terms is K, then (4K)/(101) is equal to

For the series, S=1+1/((1+3))(1+2)^2+1/((1+3+5))(1+2+3)^2+1/((1+3+5+7)) (1+2+3+4)^2 +...

For the series, S=1+1/((1+3))(1+2)^2+1/((1+3+5))(1+2+3)^2+1/((1+3+5+7))(1+2+3+4)^2 +...

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

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

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

The sum of the series 1+ 2/3+ (1)/(3 ^(2)) + (2 )/(3 ^(3)) + (1)/(3 ^(4)) + (2)/(3 ^(5)) + (1)/(3 ^(6))+ (2)/(3 ^(7))+ …… upto infinite terms is equal to :