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सिद्ध कीजिए कि `sum_(r=0)^(1000) i^(r)=1`

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सिद्ध कीजिए कि `sum_(r=0)^(1000) i^(r)=1`
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`underset(r=0)overset(1000)(sum)i^(r)=i^(0)+i^(1)+i^(2)+ . . .+i^(1000)`
`=1+i-1-i+1+ . . .+1`
`=1+(i-1-i+1+ . . .+1)=1+0`
`=1=` दायाँ पक्ष
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