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Find the sum of the series ^10 C0+^(10)C...

Find the sum of the series `^10 C_0+^(10)C_1+^(10)C_2++^(10)C_7dot`

Text Solution

Verified by Experts

Let
`S = .^(15)C_(0) + .^(15)C_(1) + .^(15)C_(2) + "……." + .^(15)C_(7)`
`:. 2S = 2(.^(15)C_(0)+ .^(15)C_(1) + .^(15)C_(2) + "……" + .^(15)C_(7))`
`= (.^(15)C_(0) + .^(15)C_(15)) + (.^(15)C_(1)+ .^(15)C_(14)) + (.^(15)C_(2) + .^(15)C_(13)) + "....." + .^(15)C_(7) + .^(15)C_(8))`
` = (.^(15)C_(0) + .^(15)C_(1) + .^(15)C_(2) + .^(15)C_(3) + "......" +( .^(15)C_(15))`
` = 2^(15)`
`:. S = 2^(14)`
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