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it-is-given-that-r-1-20-f-r-10-200-and-r-1-20-f-r-10-2-2800-find-the-value-of-r-1-20-f-r-2-

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Question Number 33153 by Rio Mike last updated on 11/Apr/18
it is given that Σ_(r=1 ) ^(20) [f(r)−10]=200 and Σ_(r=1) ^(20) [f(r)−10]^2 =2800 find the value of Σ_(r=1) ^(20) [f(r)]^2
itisgiventhat∑20r=1[f(r)−10]=200and∑20r=1[f(r)−10]2=2800findthevalueof∑20r=1[f(r)]2
Commented by prof Abdo imad last updated on 11/Apr/18
we have Σ_(r=1) ^(20) (f(r)−10) =200 ⇒ Σ_(r=1) ^(20) f(r) −200=200 ⇒ Σ_(r=1) ^(20) f(r) =400 also Σ_(r=1) ^(20) ( f^2 (r) −20f(r) +100) =2800 ⇒ Σ_(r=1) ^(20) (f(r))^2 −20 Σ_(r=1) ^(20) f(r) +2000 =2800 ⇒ Σ_(r=1) ^(20) (f(r))^2 = 800 +20 Σ_(r=1) ^(20) f(r) =800 +20 ×400 = 8800 ⇒ Σ_(r=1) ^(20) (f(r))^2 =8800.
wehave∑r=120(f(r)−10)=200⇒∑r=120f(r)−200=200⇒∑r=120f(r)=400also∑r=120(f2(r)−20f(r)+100)=2800⇒∑r=120(f(r))2−20∑r=120f(r)+2000=2800⇒∑r=120(f(r))2=800+20∑r=120f(r)=800+20×400=8800⇒∑r=120(f(r))2=8800.

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