Question

B= 2^2+ 2^3+ 2^4+....+ 2^ 98+ 2^99. Tính tổng.

Answer 1

B = 2² + 2³ + 2⁴ + ... + 2⁹⁸ + 2⁹⁹

2B = 2³ + 2⁴ + 2⁵ + ... + 2⁹⁹ + 2¹⁰⁰

2B - B = (2³ + 2⁴ + 2⁵ + ... + 2⁹⁹ + 2¹⁰⁰) - (2² + 2³ + 2⁴ + ... + 2⁹⁸ + 2⁹⁹)

B = 2¹⁰⁰ - 2²

B = 2¹⁰⁰ - 4

Answer 2

B=\(2^2+2^3+2^4+...+2^{98}+2^{99}\)

2B=\(2^3+2^4+2^5+....+2^{99}+2^{100}\)

2B-B=B= \(2^{100}-2^2\)

Answer 3

Ta có:

\(B=2^2+2^3+2^4+...+2^{98}+2^{99}\)

\(\Rightarrow2B=2^3+2^4+2^5+...+2^{100}\)

\(\Rightarrow2B-B=\left(2^3+2^4+2^5+...+2^{100}\right)-\left(2^2+2^3+2^4+...+2^{99}\right)\)

\(\Rightarrow B=2^{100}-2^2\)