Ta có: \(S=2+5+9+14+...+4949+5049\)
\(\Rightarrow2S=2.\left(2+5+9+14+...+4949+5049\right)\)
\(\Rightarrow2S=1.4+2.5+3.6+4.7+...+99.102\)
\(\Rightarrow2S=1.\left(2+2\right)+2.\left(3+2\right)+3.\left(4+2\right)+...+99.\left(100+2\right)\)
\(\Rightarrow2S=1.2+1.2+2.3+2.2+3.4+3.2+...+99.100+99.2\)
\(\Rightarrow2S=\left(1.2+2.3+3.4+...+99.100\right)+2.\left(1+2+3+...+99\right)\)
\(\Rightarrow2S=333300+9900\)
\(\Rightarrow2S=343200.\)
\(\Rightarrow S=343200:2\)
\(\Rightarrow S=171600.\)
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