CBSE Class 11-science Answered
If H is the HM between p and q then h/p+h/q
![question image](http://images.topperlearning.com/topper/new-ate/top_mob1595686747100837666674d40725-4c6a-48ca-be24-8abd683fb1d4.jpg)
Asked by mahavenkat152004 | 25 Jul, 2020, 19:49: PM
Q: If tr denotes the rth term of an H.P. for which tm = n and tn = m then tm+n =
Solution:
![straight t subscript straight m equals straight n space and space straight t subscript straight n equals straight m
rightwards double arrow fraction numerator 1 over denominator straight a plus left parenthesis straight m minus 1 right parenthesis straight d end fraction equals straight n space space and space space fraction numerator 1 over denominator straight a plus left parenthesis straight n minus 1 right parenthesis straight d end fraction equals straight m
rightwards double arrow straight a plus left parenthesis straight m minus 1 right parenthesis straight d equals 1 over straight n space space... space left parenthesis straight i right parenthesis
and comma space straight a plus left parenthesis straight n minus 1 right parenthesis straight d equals 1 over straight m space... space left parenthesis ii right parenthesis
Subtracting space left parenthesis ii right parenthesis space from space left parenthesis straight i right parenthesis space we space get
left parenthesis straight m minus 1 minus straight n plus 1 right parenthesis straight d equals 1 over straight n minus 1 over straight m
left parenthesis straight m minus straight n right parenthesis straight d equals fraction numerator straight m minus straight n over denominator mn end fraction
straight d equals 1 over mn
Putting space straight d space in space left parenthesis straight i right parenthesis comma space we space get
straight a equals 1 over mn
Now comma space straight t subscript straight m plus straight n end subscript equals fraction numerator 1 over denominator straight a plus left parenthesis straight m plus straight n minus 1 right parenthesis straight d end fraction equals fraction numerator 1 over denominator begin display style 1 over mn end style plus left parenthesis straight m plus straight n minus 1 right parenthesis begin display style 1 over mn end style end fraction equals fraction numerator 1 over denominator begin display style 1 over mn end style open parentheses 1 plus straight m plus straight n minus 1 close parentheses end fraction equals fraction numerator mn over denominator straight m plus straight n end fraction](https://images.topperlearning.com/topper/tinymce/cache/2f58ddc03d6584ac6573faeade049d4c.png)
Answered by Renu Varma | 27 Jul, 2020, 13:03: PM
Application Videos
Concept Videos
CBSE 11-science - Maths
Asked by jagathaiah.kamsali | 13 Jun, 2024, 20:20: PM
CBSE 11-science - Maths
Asked by cubesneha.2005 | 07 Feb, 2024, 00:55: AM
CBSE 11-science - Maths
Asked by prashantbharati75 | 29 Sep, 2023, 09:30: AM
CBSE 11-science - Maths
Asked by mahavenkat152004 | 25 Jul, 2020, 19:49: PM
CBSE 11-science - Maths
Asked by kien44123986 | 03 Mar, 2020, 08:33: AM
CBSE 11-science - Maths
Asked by fishtailfever | 10 Nov, 2019, 12:38: PM
CBSE 11-science - Maths
Asked by vasaya.sohil99 | 24 Sep, 2019, 11:16: AM
CBSE 11-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 13:23: PM