-->

समांतर श्रेणी

Question
CBSEHHIMAH10010196

निम्नलिखित समांतर श्रेढियों का योग ज्ञात कीजिए:
1 over 15 comma space 1 over 12 comma space 1 over 10 comma space... space 11 space पद ों space तक

Solution

यहाँ, straight a space equals space 1 over 15
straight d space equals space 1 over 12 space minus space 1 over 15 space equals space fraction numerator 5 space minus space 4 over denominator 60 end fraction space equals space 1 over 60
n =11
 straight S subscript straight n space equals space straight n over 2 space left square bracket space 2 straight a space plus space left parenthesis straight n space minus space 1 right parenthesis space straight d space right square bracket
therefore space straight S subscript 11 space equals space 11 over 2 space straight x space open square brackets space 2 space cross times space 1 over 15 space plus space left parenthesis 11 space minus space 1 right parenthesis space cross times space 1 over 60 space close square brackets
equals space 11 over 2 space cross times space open square brackets space 2 over 15 space plus space 10 space cross times space 1 over 60 space close square brackets
equals space 11 over 2 space cross times space open square brackets space 2 over 15 space plus space 1 over 6 space close square brackets space equals space 11 over 2 space cross times space open square brackets space fraction numerator 4 space plus space 5 over denominator 30 end fraction space close square brackets
equals space 11 over 2 space cross times space 9 over 30 space equals space 11 over 2 space cross times space 3 over 10 space equals space 33 over 20
  अत: दी गई A.P. के प्रथम 11 पदों का योगफल = 33 over 20