Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Updated On: 6-11-2020

Apne doubts clear karein ab Whatsapp par bhi. Try it now.

CLICK HERE

Loading DoubtNut Solution for you

Watch 1000+ concepts & tricky questions explained!

13.0 K+

600+

Text Solution

Solution :

We have <br> `T_(k)=(1)/(("kth term of "2,5,8, ...) xx("kth term of "5,8,11, ...))` <br> `=(1)/({2+(k-1)xx3}xx{5+(k-1)xx3})` <br> `=(1)/((3k-1)(3k+2))=(1)/(3){(1)/((3k-1))-(1)/((3k+2))}`. <br> `therefore T_(k)=(1)/(3){(1)/((3k-1))-(1)/((3k+2))}. " " `...(i) <br> Putting `k=1,2,3, ..., n` successively in (i), we get <br> `T_(1)=(1)/(3)((1)/(2)-(1)/(5))`<br>`T_(2)=(1)/(3)((1)/(5)-(1)/(8))` <br> `T_(3)=(1)/(3)((1)/(8)-(1)/(11))` <br> ... ... ... ... <br> ... ... ... ... <br> `T_(n) =(1)/(3){(1)/((3n-1))-(1)/((3n+2))}.` <br> Adding columnwise, we get <br> `S_(n)=(T_(1)+T_(2)+T_(3)+...+T_(n))` <br> `=(1)/(3)((1)/(2)-(1)/(3n+2))=(n)/(2(3n+2)).`