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Question Number 100179 by bobhans last updated on 25/Jun/20
Answered by john santu last updated on 25/Jun/20
ToolsA+B=12(A+A2−B)+12(A−A2−B)⇒m+m2−1=12(m+1)+12(m−1)∑nm=1112(m+1)+12(m−1)=2∑nm=11m+1+m−1=12∑nm=1m+1−m−1=12∑n+2m=3m−1−12∑nm=1m−1=12{∑nm=3m−1+n+n+1−(0+1+∑nm=3m−1)}=12(n+1+n−1)◼
Answered by maths mind last updated on 25/Jun/20
(m+1+m−1)2=2m+2m2−1⇒m+m2−1=(m+1+m−1)22=m+m2−1=m+1−m−12Σ1m+m2−1=∑nm=12m+1+m−1=Σ2(m+1−m−1)2=12.∑nm=1(m+1−m−1)=n+1+n−12
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