10.计算:
(1) $-2^2 × (-\frac{1}{2})^3 - |-2|^3 + (-\frac{1}{2})$;
(2) $(-3)^2 ÷ 2\frac{1}{4} × (-\frac{2}{3}) + 4 + 2^2 × (-\frac{8}{3})$;
(3) $(\frac{5}{6} - \frac{3}{4}) × 12 ÷ (-2^2) + |-1|$;
(4) $-2^4 - (-2)^2 - 3^2 ÷ (-1\frac{1}{2})$;
(5) $-2^5 ÷ (-4) × (\frac{1}{2})^2 - 12 × (-15 + 2^4)^3$;
(6) $2\frac{2}{9} × (-1\frac{1}{2})^3 - (-1.2)^2 ÷ 0.4^2$。
(1) $-2^2 × (-\frac{1}{2})^3 - |-2|^3 + (-\frac{1}{2})$;
(2) $(-3)^2 ÷ 2\frac{1}{4} × (-\frac{2}{3}) + 4 + 2^2 × (-\frac{8}{3})$;
(3) $(\frac{5}{6} - \frac{3}{4}) × 12 ÷ (-2^2) + |-1|$;
(4) $-2^4 - (-2)^2 - 3^2 ÷ (-1\frac{1}{2})$;
(5) $-2^5 ÷ (-4) × (\frac{1}{2})^2 - 12 × (-15 + 2^4)^3$;
(6) $2\frac{2}{9} × (-1\frac{1}{2})^3 - (-1.2)^2 ÷ 0.4^2$。
答案:(1)$-8$ (2)$-\frac{28}{3}$ (3)$\frac{3}{4}$ (4)$-14$ (5)$-10$ (6)$-16\frac{1}{2}$
11.(2025·酒泉期中)数学课上老师讲解了一道题:计算:$1+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9$.
解:令$S=1+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9$,①
则$2S=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}$,②
②−①,得$S=2^{10}−1$.
根据以上方法,计算:
(1)$1+2^1+2^2+2^3+2^4+…+2^{2025}$;(写出过程,结果用幂表示)
(2)$1+3+3^2+3^3+3^4+…+3^{2025}=$
解:令$S=1+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9$,①
则$2S=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}$,②
②−①,得$S=2^{10}−1$.
根据以上方法,计算:
(1)$1+2^1+2^2+2^3+2^4+…+2^{2025}$;(写出过程,结果用幂表示)
(2)$1+3+3^2+3^3+3^4+…+3^{2025}=$
$\frac{3^{2026}-1}{2}$
.(结果用幂表示)答案:(1)解:令$S=1+2^1+2^2+2^3+2^4+…+2^{2025}$,①
则$2S=2+2^2+2^3+2^4+2^5+…+2^{2026}$,②
②−①,得$S=2^{2026}-1$.
(2)$\frac{3^{2026}-1}{2}$
则$2S=2+2^2+2^3+2^4+2^5+…+2^{2026}$,②
②−①,得$S=2^{2026}-1$.
(2)$\frac{3^{2026}-1}{2}$