对任意不为0的自然数a,b规定a⊗b=2×a+b,若有:a⊗2a⊗3a⊗4a⊗5a⊗6a⊗7a⊗8a⊗9a=3039,求a=_.
问题描述:
对任意不为0的自然数a,b规定a⊗b=2×a+b,若有:a⊗2a⊗3a⊗4a⊗5a⊗6a⊗7a⊗8a⊗9a=3039,求a=______.
答
因为a*b=2×a+b,所以:a*2a=2a+2a=4a,4a*3a=4a×2+3a=11a,11a*4a=11a×2+4a=26a,26a*5a=26a×2+5a=57a,57a*6a=57a×2+6a=120a,120a*7a=120a×2+7a=247a,247a*8a=247a×2+8a=502a,502a*9a=502a×2+9a=1013a,...