若 11×3+13×5+15×7+…+1(2n−1)(2n+1)的值为1735,则正整数n的值是( ) A.16 B.17 C.18 D.19
问题描述:
若
+1 1×3
+1 3×5
+…+1 5×7
的值为1 (2n−1)(2n+1)
,则正整数n的值是( )17 35
A. 16
B. 17
C. 18
D. 19
答
原式=
(1-1 2
)+1 3
(1 2
-1 3
)+…+1 5
(1 2
-1 2n−1
)1 2n+1
=
(1-1 2
+1 3
-1 3
+…+1 5
-1 2n−1
)1 2n+1
=
(1-1 2
)1 2n+1
=
×1 2
2n 2n+1
=
n 2n+1
=
.17 35
解得:n=17.