问题
计算题
(1)计算:C33+C43+C53+…+C103
(2)证明:Ank+kAnk﹣1=An+1k.
答案
解:(1)∵Cmn+Cm﹣1n=Cmn+1,
∴原式=C44+C43+C53+…+C103
=C54+C53+C63+…+C103
=C64+C63+C73+…+C103
=…=C104+C103=C114=330
(2)证明:∵
∴左边=+k
=
=
=An+1k=右边
(1)计算:C33+C43+C53+…+C103
(2)证明:Ank+kAnk﹣1=An+1k.
解:(1)∵Cmn+Cm﹣1n=Cmn+1,
∴原式=C44+C43+C53+…+C103
=C54+C53+C63+…+C103
=C64+C63+C73+…+C103
=…=C104+C103=C114=330
(2)证明:∵
∴左边=+k
=
=
=An+1k=右边