The method to obtain the answer of (n + 1)(n + 2)(n + 3)(n + 4) / 24
As we know, when n = 1, the answer = 5 that is 1 + 1 + 1 + 1 + 1;\nwhen n = 2, the answer = 15 that is 1 + 2 + 3 + 4 + 5\n         n = 3, the answer = 35, that 
As we know, when n = 1, the answer = 5 that is 1 + 1 + 1 + 1 + 1;\nwhen n = 2, the answer = 15 that is 1 + 2 + 3 + 4 + 5\n         n = 3, the answer = 35, that is 1 + 3 + 6 + 10 + 15\n\t\t ....\n\t\t we can set the f(n) = fn(1) + fn(2) + fn(3) + fn(4) + fn(5)\n\t\t fn(1) = 1; \n\t\t fn(2) = 1 + fn-1(2), so fn(2) = 1+1+... + 1 = n;\n\t\t fn(3) = fn-1(3) + fn(2) = n + fn-1(3), so fn(3) = 1 + 2 + ... + n = n(n+1)/2;\n\t\t as usual, fn(4) = 1*2/2 + 2 * 3/2 + 3*4/2 +... + n(n+1)/2 = n(n+1)(n+2)/6;\n\t\t fn(5) = 1*2*3/6 + 2*3*4/6 +...+n(n+1)(n+2)/6 = n(n+1)(n+2)(n+3)/24;\n\t\t so f(n) = fn(1)+fn(2)+fn(3)+fn(4)+fn(5) = 1 + n + n(n+1)/2 + n(n+1)(n+2)/6+n(n+1)(n+2)(n+3)/24 = (n+1)(n+2)(n+3)(n+4)/24\n\t\t
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