If H is the HM between p and q then h/p+h/q

Asked by mahavenkat152004 | 25th Jul, 2020, 07:49: PM

Expert Answer:

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

Answered by Renu Varma | 27th Jul, 2020, 01:03: PM