Let `S=1/(1.4)+1/(4.7)+1/(7.10)+.....+ n ` terms observe the following lists

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

Find the sum of the series : (1)/(1.4)+(1)/(4.7)+(1)/(7.10)+.... to n terms.

2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

(1)/(1 . 4 . 7)+(1)/(4 .7 . 10)+(1)/(7 . 10 . 13)+.. . to n terms =

Using mathematical induction prove that 1/(1.4)+1/(4.7)+1/(7.10)+.......+1/((3n-2)(3n+1))=n/(3n+1) for all n in N

For all ninNN , prove by principle of mathematical induction that, (1)/(1*4)+(1)/(4*7)+(1)/(7*10)+ . . . to terms =(n)/(3n+1) .

2.4+4.7+6.10+....(n-1)terms=

" Find the sum of series " (3)/(1.4)+(3)/(4.7)+(3)/(7.10)+.... " up to "20" terms."

(1)/(1*4*7)+(1)/(4*7*10)+(1)/(7*10*13)+

Using the principle of finite Mathematical Induction prove the following: (iii) 1/(1.4) + 1/4.7 + 1/7.10 + ……… + "n terms" = n/(3n+1) .