Tính : ( 1 +1/3 ) x ( 1 + 1/8 ) x ( 1+1/15 ) x … x (1 + 1/9999 ) 10/09/2021 Bởi Liliana Tính : ( 1 +1/3 ) x ( 1 + 1/8 ) x ( 1+1/15 ) x … x (1 + 1/9999 )
Giải thích các bước giải: ( 1 + 1313 ) x ( 1 + 1818 ) x ( 1 + 115115 ) x … x ( 1 + 1999919999 ) = 4343 x 9898 x 16151615 x … x 100009999100009999 = 2x2x3x3x4x4x...x100x1001x3x2x4x3x5x...x99x1012x2x3x3x4x4x…x100x1001x3x2x4x3x5x…x99x101 = (2x3x4x...x100)x(2x3x4x...x100)(2x3x4x...x99)x(3x4x5x...x101)(2x3x4x…x100)x(2x3x4x…x100)(2x3x4x…x99)x(3x4x5x…x101) = 100x2101100×2101 = 200101200101 Bình luận
Đáp án: Giải thích các bước giải: ( 1 + $\frac{1}{3}$ ) x ( 1 + $\frac{1}{8}$ ) x ( 1 + $\frac{1}{15}$ ) x … x ( 1 + $\frac{1}{9999}$ ) = $\frac{4}{3}$ x $\frac{9}{8}$ x $\frac{16}{15}$ x … x $\frac{10000}{9999}$ = $\frac{2 x 2 x 3 x 3 x 4 x 4 x … x 100 x 100}{1 x 3 x 2 x 4 x 3 x 5 x … x 99 x 101}$ = $\frac{( 2 x 3 x 4 x … x 100 )x ( 2 x 3 x 4 x … x 100 )}{( 2 x 3 x 4 x … x 99 ) x ( 3 x 4 x 5 x … x 101 )}$ = $\frac{100×2}{101}$ = $\frac{200}{101}$ Bình luận
Giải thích các bước giải:
( 1 + 1313 ) x ( 1 + 1818 ) x ( 1 + 115115 ) x … x ( 1 + 1999919999 )
= 4343 x 9898 x 16151615 x … x 100009999100009999
= 2x2x3x3x4x4x...x100x1001x3x2x4x3x5x...x99x1012x2x3x3x4x4x…x100x1001x3x2x4x3x5x…x99x101
= (2x3x4x...x100)x(2x3x4x...x100)(2x3x4x...x99)x(3x4x5x...x101)(2x3x4x…x100)x(2x3x4x…x100)(2x3x4x…x99)x(3x4x5x…x101)
= 100x2101100×2101
= 200101200101
Đáp án:
Giải thích các bước giải:
( 1 + $\frac{1}{3}$ ) x ( 1 + $\frac{1}{8}$ ) x ( 1 + $\frac{1}{15}$ ) x … x ( 1 + $\frac{1}{9999}$ )
= $\frac{4}{3}$ x $\frac{9}{8}$ x $\frac{16}{15}$ x … x $\frac{10000}{9999}$
= $\frac{2 x 2 x 3 x 3 x 4 x 4 x … x 100 x 100}{1 x 3 x 2 x 4 x 3 x 5 x … x 99 x 101}$
= $\frac{( 2 x 3 x 4 x … x 100 )x ( 2 x 3 x 4 x … x 100 )}{( 2 x 3 x 4 x … x 99 ) x ( 3 x 4 x 5 x … x 101 )}$
= $\frac{100×2}{101}$
= $\frac{200}{101}$