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If the m^th term of an AP is 1/n and n^th term of an ap is 1/m than prove that Smn=1/2(mn+1)

Posted by Sarthak Singh 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Utkarsh Singh 6 years, 10 months ago

According to the question A+(m-1)d=1/n-------(1) A+(n-1)d=1/m-------(2) (1)-(2) (m-1)d-(n-1)d=1/n-1/m Taking d common in LHS and taking LCM in RHS d(m-1-n+1)=(m-n)/mn d(m-n)=(m-n)/mn d=1/mn--------------(3) Using (3) in (1) A+(m-1)/mn=1/n A+1/n-1/mn=1/n A=1/mn-------------(4) Sum of mn terms=mn(2A+(mn-1)d)/2 =mn(2/mn+(mn-1)/mn)/2 =mn(2/mn+1-1/mn)/2 =mn(1/mn+1)/2 =mn(1+mn/2mn) =(1+mn)/2

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CBSE > Class 10 > Mathematics