Question

Find the sum of the coefficients ${}^{15}{C}_0{+}^{15}{C}_1{+}^{15}{C}_2{+}^{15}{C}_3+...{+}^{15}{C}_7$.

Answer 1

Given: ${}^{15}{C}_0{+}^{15}{C}_1{+}^{15}{C}_2{+}^{15}{C}_3+...{+}^{15}{C}_7$

To Find: Sum of the given coefficients.

Here, the series is exactly half series $\left(8\text{terms}\right)$.

As the full series $\left(16\text{terms}\right)$ will be ${}^{15}{C}_0{+}^{15}{C}_1{+}^{15}{C}_2{+}^{15}{C}_3+...{+}^{15}{C}_{15}$.

So, the sum of the given series will be exactly half of the full series which is $2^{15}$.

So, the sum of the given series will be $2^{14}$.