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Grade: 11
        If a1,a2,a3,....,an are in AP,ai>0 for all i,show that 1/(√a1+√a2)+1/(√a2+√a3)+.....+1/(√an-1 + √an)=(n-1)/(√a1+√an)
one year ago

Answers : (2)

moumi roy
91 Points
							1/(√a1+√a2)+1/(√a2+√a3)+.....+1/(√an-1 + √an)
(√a2-√a3)/(a2-a3)+...(√an-1-√an)/({an-1}-an)...[rationalising]=(√a1-√a2)/(a1-a2)+
(√a2-√a3)/d...-(√an-1-√an)/d...[(tn)-(tn-1)=d=comn diff]=-(√a1-√a2)/d-
all the conecutive term will cancel excp
√an)/d=-(a1-an)/(√a1+√an)d=-(√a1-=-(a1-a1-(n-1)d)/(√a1+√an)d=(n-1)/(√a1+√an)
one year ago
Alwin
19 Points
							1/(√a1+√a2)+1/(√a2+√a3)+.....+1/(√an-1 + √an) (√a2-√a3)/(a2-a3)+...(√an-1-√an)/({an-1}-an)...[rationalising]=(√a1-√a2)/(a1-a2)+ (√a2-√a3)/d...-(√an-1-√an)/d...[(tn)-(tn-1)=d=comn diff]=-(√a1-√a2)/d- all the conecutive term will cancel excp√an)/d=-(a1-an)/(√a1+√an)d=-(√a1-=-(a1-a1-(n-1)d)/(√a1+√an)d=(n-1)/(√a1-√an)
						
one year ago
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