​ The value of ∑n=0^1947 1/2^n+√2^1947 is equal to (a) 487/√2^1945 (b) 1946/√2^1947 (c) 1947/√2^1947 (d) 1948/√2^1947​

Question

The value of \(\displaystyle\sum_{n=0}^{1947}\;\frac{1}{2^n+\sqrt{2^{1947}}}\) is equal to

∑_n=0¹⁹⁴⁷ 1/2ⁿ+√2¹⁹⁴⁷

(a) \(\frac{487}{\sqrt{2^{1945}}}\)

487/√2¹⁹⁴⁵

(b) \(\frac{1946}{\sqrt{2^{1947}}}\)

1946/√2¹⁹⁴⁷

(c) \(\frac{1947}{\sqrt{2^{1947}}}\)

1947/√2¹⁹⁴⁷

(d) \(\frac{1948}{\sqrt{2^{1947}}}\)

1948/√2¹⁹⁴⁷

Answer 1

Answer is :  (a) \(\frac{487}{\sqrt{2^{1945}}}\)

We have,