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in Binomial theorem by (160 points)
edited by

If nC7 = n !/ r ! (n - r) ! then the sum of the series 1 + nC1 + n+1C2 + n+2C3 ...... + n+r-1Cr is equal to

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1 Answer

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by (32.0k points)

1 + nC1 + n+1C2 + n+2C3+...... + n + r - 1C

 = nC0 + nC1 + n+1C2 + n+2C3 + ........ + n + r - 1Cr (\(\because\) nC0 = 1)

= n+1C1 + n+1C2 + n+2C3+......n+r-1Cr (\(\because\) nCr + nCr+1 = n+1Cr+1)

= n+2C2 + n+2C3+....n+r-1Cr

= n+r-1Cr-1 + n+r-1Cr

= n+rCr

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