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प्रश्न
The sum of the series `sum_(r = 0)^10 ""^20C_r` is `2^19 + (""^20C_10)/2`
पर्याय
True
False
उत्तर
This statement is False.
Explanation:
`sum_(r = 0)^10 ""^20C_r = ""^20C_0 + ""^20C_1 + ""^20C_2 + ""^20C_3 + ... + ""^20C_10`
= `""^20C_0 + ""^20C_1 + ... + ""^20C_10 + ""^20C_10 + ""^20C_11 + ... ""^20C_20`
= `-(""^20C_11 + ... + ""^20C_20)`
= `2^20 - (""^620C_11 + ... + ""^620C_20)`
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