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how 2 solve dis...??

1+(1+(1/2))+(1+(1/2)+(1/4)) n terms

plz ...plz ...tell me dis..

6 years ago


Answers : (1)


Dear srishti

sum of nterms can be written as  as n+n-1/2 + n-2/4-----+1/2n-1

which is sum of nterms of an AGP

The sum Sn of first n terms of an A.G. P. is obtained in the   following way :


Sn = ab + (a + d)br + (a + 2d)br2 +.........+(a + (n - 2)d)brn-2 + (a + (n - 1)d)brn-1

Multiply both sides by r, so that

r Sn = abr + (a + d)br2+.........+(a + (n - 3)d)brn-2 + (a + (n - 2)d)brn-1 + (a + (n - 1)d)brn

Subtracting, we get

(1 - r)Sn = ab + dbr + dbr2 +.......+dbrn - 2 + dbrn - 1 - (a + (n - 1)d)brn

= ab + dbr/(1–rn–1)/(1–r) – (a+(n–1)d)brn => Sn = ab/1–r + dbr(1–rn–1)/(1–r)2 – (a+(n–1)d)brn/1–r




So Sn = 2n+(-1)*0.5*1(1-0.5n-1)*4-2n

=>Sn = 2n-2(1-0.5n-1)-2n

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6 years ago

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