" 7."S=(1)/(1.2)+(1)/(2.3)+(1)/(3.4)+........." n term "

(1)/(1.2)+(1)/(2.3)+(1)/(3.4)+... to n terms

Let S = (1)/( 1.4) + (1)/( 4.7) + (1)/(7.10) + .....n terms, Observe the following lists. {:("List-I","List-II"),("A)" underset(n to prop) (Lt) S=, "1)"0 ),("B)" underset(n to 0 ) (Lt) S=,"2)" 3//10),("C)" underset(n to 3) (Lt) S=,"3)"1//3),("D)" underset(n to 4) (Lt) S=,"4)"1),(,"5)"4//13):}

1/(1.2)+1/(2.3)+1/(3.4)+... to n terms

Find sum the series (n)/(1.2*3)+(n-1)/(2.3*4)+(n-2)/(3.4*5)+......... up to n terms..-

Find the sum to n terms of the series , (1)/(1.2)+(1)/(2.3)+(1)/(3.4)+.... ?

Sum of n terms of (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + …. is

If S_(n) = (1)/(1.4)+(1)/(4.7) + (1)/(7.10) +……. to n terms, then lim_(n rarr oo) S_(n) equals :

If S_(1), S_(2), S_(3),….., S_(n) are the sum of infinite geometric series whose first terms are 1,3,5…., (2n-1) and whose common rations are 2/3, 2/5,…., (2)/(2n +1) respectively, then {(1)/(S_(1) S_(2)S_(3))+ (1)/(S_(2) S_(3) S_(4))+ (1)/(S_(3) S_(4)S_(5))+ ........."upon infinite terms"}=

If S_(1), S_(2), S_(3),….., S_(n) are the sum of infinite geometric series whose first terms are 1,3,5…., (2n-1) and whose common rations are 2/3, 2/5,…., (2)/(2n +1) respectively, then {(1)/(S_(1) S_(2)S_(3))+ (1)/(S_(2) S_(3) S_(4))+ (1)/(S_(3) S_(4)S_(5))+ ........."upon infinite terms"}=

1+(1+2)/(2)+(1+2+3)/(3) +(1+2+3+4)/(4)+.. . to n terms =