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Tổng nó rất là cao không thể rút gọn nữa có vẻ như bài này quá khó về kết quả tổng
Ta có A có 100 số hạng.
A+100 = 101+102+103+...+10100
\(\Rightarrow\)10 (A+100)= 102+103+...+10101
\(\Rightarrow\)9(A+100)=10101-10\(\Rightarrow\)A=\(\frac{10^{101}-10}{9}-100\)
Tổng quát nếu số hạng cuối của A có n chữ số thì A=\(\frac{10^{n+1}-10}{9}-n\)
a) 100 - 99 + 98 -97 + 96 -95 +...+ 4-3 + 2
= (100 - 99) + (98 -97) + (96 - 95) +...+ (4-3) +2 (gồm 49 cặp và 1 số hạng)
= 1+1+1+....+1 +2
= 49 x 1 + 2 = 51
b) 100 - 5-...-5 - 5 (20 số 5)
= 100 - 20 x 5 = 0
c) 99 - 9 - 9 -... - 9 -9 (11 số 9)
=99 - 11 x 9 = 0
d) 2011 + 2011+2011+2011 - 2008 x 4
= 2011 x 4 - 2008 x 4
= 4 x (2011 - 2008)
= 4 x 3
=12
=(1+98-99-100)+(2-3-4+5)+(6-7-8+9)+...+(95-96-97+98)
=-100+0+0+0+0+0.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................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mk ko bít làm bài này
mk gởi ý cho bn nnha :
L=( 1.98 +98.1)+(2.97+97.2)+(3.96+96.3)+ ........ ( bn cứ tính như vậy theo từng cặp một ) rùi => số cặp
= 98.(1+1)+(97.(2+2))+..............( tính ra như vậy)
=tính ra théo như tính tổng
=kq
cách 2 tính nhanh mà dài lắm mk nhác viết