Symbiosis National Aptitude Test SNAP 2019 Paper

Question : 40 of 110

Marks: +1, -0

Find the unit's place digit of

(1!)^{1!} + (2!)^{2!} + (3!)^{3!}

+ ... +

(100!)^{100!}

Solution:

(1!)^{1!} + (2!)^{2!} + (3!)^{3!}

+ ... +

(100!)^{100!}

(1)^1 + (1 × 2)^{1×2}

(1 × 2 × 3)^{1×2×3}

(1 × 2 × 3 × 4)^{1×2×3×4}

(1 × 2 × 3 × 4 × 5)^{1×2×3×4×5}

+ ... +

(100!)^{100!}

Sum of unit digits
= 1 + 4 + 6 + 6 + 0 ... + 0 = 17
Hence, units place digit = 7

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